BITSAT 2010
Exam BITSAT
Year 2010
Subject Mathematics
Chapter Trigonometric Equations BITSAT 2010 · Mathematics · Trigonometric Equations
If (12 ^2 θ-31 coses θ+32=0), then the value of ( θ) is
If (12 \cot ^2 \theta-31 \operatorname{coses} \theta+32=0), then the value of (\sin \theta) is
Options A (3 5 \frac{3}{5} 5 3 B (2 3 \frac{2}{3} 3 2 − 2 3 \frac{-2}{3} 3 − 2 C (4 5 \frac{4}{5} 5 4 3 4 \frac{3}{4} 4 3 D (\pm 1 2 \frac{1}{2} 2 1 Correct answer A. (3 5 \frac{3}{5} 5 3
Step-by-step solution
(
12 cot 2 θ − 31 cosec θ + 32 = 0 ⇒ 12 ( cosec 2 θ − 1 ) − 31 cosec θ + 32 = 0 and ⇒ 12 cosec 2 θ − 31 cosec θ + 20 = 0 and ⇒ 12 cosec 2 θ − 16 cosec θ − 15 cosec θ + 20 = 0 and ⇒ ( 4 cosec θ − 5 ) ( 3 cosec θ − 4 ) = 0 and ⇒ cosec θ = 5 4 , 4 3 ; ∴ sin θ = 4 5 , 3 4 \begin{aligned}
& 12 \cot ^2 \theta-31 \operatorname{cosec} \theta+32=0 \\
& \Rightarrow 12\left(\operatorname{cosec}^2 \theta-1\right)-31 \operatorname{cosec} \theta+32=0 \\
\text{\text{ and } } \Rightarrow \quad 12 \operatorname{cosec}^2 \theta-31 \operatorname{cosec} \theta+20=0 \\
\text{ and } \Rightarrow \quad 12 \operatorname{cosec}^2 \theta-16 \operatorname{cosec} \theta-15 \operatorname{cosec} \theta+20=0 \\
\text{ and } \Rightarrow \quad(4 \operatorname{cosec} \theta-5)(3 \operatorname{cosec} \theta-4)=0 \\
\text{ and } \Rightarrow \quad \operatorname{cosec} \theta=\frac{5}{4}, \frac{4}{3}; \therefore \sin \theta=\frac{4}{5}, \frac{3}{4}
\end{aligned} and ⇒ 12 cosec 2 θ − 31 cosec θ + 20 = 0 and ⇒ 12 cosec 2 θ − 16 cosec θ − 15 cosec θ + 20 = 0 and ⇒ ( 4 cosec θ − 5 ) ( 3 cosec θ − 4 ) = 0 and ⇒ cosec θ = 4 5 , 3 4 ; ∴ sin θ = 5 4 , 4 3 12 cot 2 θ − 31 cosec θ + 32 = 0 ⇒ 12 ( cosec 2 θ − 1 ) − 31 cosec θ + 32 = 0 )
Practice Trigonometric Equations on Quantrex Academy →
← Previous question If \( θ=-(1)/(2)\) and \( θ=1 / 3 \), then \(θ=\)Next question → \( 20^ ^ ∘ + 40^ ^ \ circ + 3 20^ ^ ∘ 40^ ^ ∘ \) is equal to
More from Trigonometric Equations
Number of solutions of equations 9 θ= θ in the interval [0,2 π] is BITSAT 2024 The range of (8 θ+6 θ)^2+2 is BITSAT 2024 General solution of 5 θ= 2 θ is BITSAT 2023 If ^2 θ=(4)/(3) , then the general value of θ is BITSAT 2023 The sum of all the solution of the equation θ ((π)/(3)+θ) ((π)/(3)-θ)=(1)/(4), θ ∈[0,6 π] BITSAT 2022 If y=(2 α)/(1+ α+ α) , then value of (1- α+ α)/(1+ α) is BITSAT 2021 The value of [n π+(-1)^ n (π)/(4)], n ∈ I is BITSAT 2020 The least positive non-integral solution of the equation π(x^ 2 +x)= π x^ 2 is BITSAT 2020 The number of real numbers λ for which the equality ( ( λα ))/(sinα) - ( ( λα ))/(cosα) =… BITSAT 2019 Equation x + (t + x) + (t - x) = 2 has real solution, then t can be BITSAT 2018 The general solution of x - 3 2x + 3x = x - 3 2x + 3x & is BITSAT 2017 If θ_ 1 + θ_ 2 + θ_ 3 =3, then θ_ 1 + θ_ 2 + θ^ 3 = BITSAT 2016 If ( x)= ( x) , then 2 x is equal to: BITSAT 2016 The general solution of the equation 2 x+2 x+2 x+1=0 is BITSAT 2016 The solution of (2 x-1)(3+2 x)=0 in the interval 0 ≤ x ≤ 2 π is BITSAT 2014 If 7 θ= θ- 4 θ, then the general value of θ is BITSAT 2013
Full Trigonometric Equations list
Trigonometric Equations JEE Maths PYQs JEE Mathematics PYQs
All BITSAT PYQs
