NDA PYQ Trigonometric Ratios & Identities - Chapter-wise Questions with Solutions

About Trigonometric Ratios & Identities PYQs

Trigonometric Ratios & Identities has 295 previous year questions in the Quantrex Academy NDA Mathematics bank. The 220 questions in this list come from NDA (220), spanning 2013 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

NDA Trigonometric Ratios & Identities PYQs with Solutions

About Trigonometric Ratios & Identities PYQs

Questions by year (this list)

Trigonometric Ratios & Identities questions with solutions

If θ lies in the fourth quadrant and 3 θ+4=0 , then what is the value of 2θ+ 2θ ?

If α+ β=0= α+ β , α≠β then what is a value of 2α+ 2β+2 (α+β) ?

If 2 4β= 2α+ 2α , then which one of the following is a possible value of (α+β) ?

If x= θ- θ and y= θ+ θ , then which one of the following is correct ?

If θ=(1)/(3) , then what is the value of ((θ)/(2)) ((3θ)/(2)) ?

If A and B are acute angles such that 2A+2B=π , then what is the maximum value of A· B ?

x+ 3 x is maximum when x is equal to

In a triangle ABC , A= B+ C then what is ((B)/(2))+ ((B)/(2))equal to ?

If α and β are complementary angles such that α-β=(π)/(6) and m β=n α , then what is ((m+n)/(m-n)) equal to ?

For the following two (02) items: Let A + B = p and A + B = q . What is (p^2 - q^2)/(p^2 + q^2) equal to?

For the following two (02) items: Let p = cosec\, 20° and q = cosec\, 70° . What is (p^2 + q^2)/(p^2 q^2) equal to?

For the following two (02) items: Let A + B = p and A + B = q . What is (p)/(q) equal to?

For the following two (02) items: Let p = cosec\, 20° and q = cosec\, 70° . What is ( 3 \,p 4 - (q)/(4)) equal to?

Consider the following for the three (03) items that follow: Let p = 35° , q = 25° and r = (-95°) . What is (p + q + r) equal to?

Consider the following for the three (03) items that follow: Let p = 35° , q = 25° and r = (-95°) . What is (pq + qr + rp) equal to?

Consider the following for the three (03) items that follow: Let p = 35° , q = 25° and r = (-95°) . What is (p^2 + q^2 + r^2) equal to?

Consider the following for the two (02) items that follow: Let p = | α - (α - 90°)| . What is the maximum value of p ?

Consider the following for the two (02) items that follow: Let p = | α - (α - 90°)| . What is the minimum value of p ?

Consider the following for the three (03) items that follow: Let p = 2α - α and q = α - 2α . What is (p/q) equal to?

Consider the following for the three (03) items that follow: Let p = 2α - α and q = α - 2α . What is (p + q) equal to?

Consider the following for the three (03) items that follow: Let p = 2α - α and q = α - 2α . What is ^2α equal to?

Consider the following for the two (02) items that follow: Let 2 α + α = 2 , where 0 What is α equal to?

Consider the following for the two (02) items that follow: Let 2 α + α = 2 , where 0 What is 2 2α + 2α equal to?

In a triangle ABC, A+ B+ C=k What is the value of A B C ?

What is 12^ ^ ∘ 48^ ^ ∘ equal to?

Consider the following numbers: A. 22.5^ ^ ∘ B. 22.5^ ^ ∘ C. 22.5^ ^ ∘ - 22.5^ ^ ∘ How many of the above are irrational numbers?

What is the maximum value of the a x+b x+c ?

If p (θ-30^ ^ ∘ )=q (θ+120^ ^ ∘ ), then what is ((p+q))/((p-q)) equal to? equal to?

If (x)/( θ)=(y)/( ((2 π)/(3)-θ))=(z)/( ((2 π)/(3)+θ)) then what is x+y+z equal to?

If A B C is a triangle, then what is the value of the determinant | array ccc C & ~B & 0 ~A & 0 & ~B 0 & (~B+C) & C array | ?

What is ( 9^ ^ ∘ - 9^ ^ ∘ ) equal to?

ABC is a triangle such that angle C=60^ ^ ∘ , then what is A+ B ( A-B 2 ) equal to?

If f(θ)=(1)/(1+ θ) and α+β=(5 π)/(4) , then what is the value of f(α) f(β) ?

If α and β are the roots of the equation x^2-6 x+8=0 , then what is the value of (2 α+2 β) ?

What is the value of 65^ ^ ∘ +2 45^ ^ ∘ -2 40^ ^ ∘ - 25^ ^ ∘ ?

What is 17^ ^ ∘ - 17^ ^ ∘ 17^ ^ ∘ + 17^ ^ ∘ equal to?

What is 3 10^ ^ ∘ - 10^ ^ ∘ 25^ ^ ∘ 25^ ^ ∘ equal to?

What is the value of 10^ ^ ∘ · 50^ ^ ∘ + 50^ ^ ∘ . 250^ ^ ∘ + 250^ ^ ∘ · 10^ ^ ∘ equal to?

If α=(1)/(7), β= 1 10 ; 0 < α, β < (π)/(2) then what is the value of (α+2 β) ?

A function is defined by f(x)=π+ ^2 x What is the period of the function?

Let p= ((π)/(5)) ((2 π)/(5))and q= ((4 π)/(5)) ((8 π)/(5)). What is the value of p+q ?

Let p= ((π)/(5)) ((2 π)/(5))and q= ((4 π)/(5)) ((8 π)/(5)). What is the value of p q ?

Let p=(1)/(3)-( 3 x)/( x) and q=1-3 ^2 x, 0 < x < π, x ≠ (π)/(2) . What is pq equal to

Let x+ y= 3 ( y- x) ; x+y=(π)/(2) , 0 < x, y < (π)/(2) What is a value of 3 x+ 3 y ?

Let x+ y= 3 ( y- x) ; x+y=(π)/(2) , 0 < x, y < (π)/(2) What is a value of ^3 x+ ^3 y ?

Let p=(1)/(3)-( 3 x)/( x) and q=1-3 ^2 x, 0 < x < π, x ≠ (π)/(2) . For how many values of x does (1)/(p) become zero?

Paragraph: Given that x+ x+ x+ x+ x+cosec x=7 Question: The given equation can be reduced to

Paragraph: Let β be the GM of α and α ; γ be the AM of α and α Question: What is 2 β equal to?

Paragraph: Given that x+ x+ x+ x+ x+cosec x=7 Question: If 2 x=a-b c , where a and b are natural numbers and c is prime number, then what is the value of a-b+2 c ?

Paragraph: Let f(x)= [π^2] x+ [-π^2] x where [.] is a greatest integer function. Question: What is f ((π)/(2))equal to?

If f(x)=x (4 x²-3) , then what is f( θ)equal to?

Paragraph: Let f(x)= [π^2] x+ [-π^2] x where [.] is a greatest integer function. Question: What is f ((π)/(4))equal to?

Paragraph: Let β be the GM of α and α ; γ be the AM of α and α Question: What is the value of of 2 γ ?

What is the value of cosec (-(73 π)/(3))?

What is the value of ((5 π)/(17))+ ((7 π)/(17))+2 ((11 π)/(17)) ((π)/(17)) ?

What is the value of ((3 π)/(8))?

What is the value of ^2 165^ ^ ∘ + ^2 165^ ^ ∘ ?

If x=(25)/(24) and x lies in the fourth quadrant, then what is the value of x+ x ?

What is 36^ ^ ∘ - 72^ ^ ∘ equal to?

If f(α)= ^2 α-1 , then what is (f(α)+f(β))/(1-f(α) f(β)) equal to?

What is the value of (2 n π+(5 π)/(6)) (2 n π-(5 π)/(6)), where n ∈ Z ?

In a triangle A B C , A- B- C=0 What is angle B equal to?

If (45^ ^ ∘ +θ)=1+ 2 θ , where -(π)/(4) < θ < (π)/(4) , then what is the value of 2 θ ?

Let 2 θ= 3 θ , where θ is acute angle. What is the value of 1+4 θ ? (. given that . 18^ ^ ∘ = 5 -1 4 )

If θ=-(5)/(12) , then what can be the value of θ ?

What is the value of ^4 (7 π)/(8)+ ^4 (5 π)/(8) ?

What is ^2 \ left((π)/(4)+θ)- ^^2\ left( (π)/(4)- θ) equal to?

If α+ β=1- α · β , where then which of the following is one of the values of (α+β) ?

If (1+ θ)(1+ 9 θ)=2 , then what is the value of (10 θ) ?

What is the value of 0^ ^ ∘ + 10^ ^ ∘ + 20^ ^ ∘ + 30^ ^ ∘ +….+ 360^ ^ ∘ ?

What is the maximum value of the function f(x)=(1)/( x+ x) , where 0 < x < (π)/(2) ?

What is the maximum value of 3( x- x)+4( ^3 x..- ^3 x) ?

If α+β=(π)/(4) and 2 α=1 , then what is 2 β equal to?

What is value of ^2 15^ ^ ∘ + ^2 15^ ^ ∘ ?

Let the equation x · cosec x=p have a solution, where p is a positive real number. What should be the smallest value of p ?

Let A B C be a triangle. If 2 A+ 2 B+ 2 C=-1 then which one of the following is correct?