Q: Let A, B and C are the angles of a triangle and A 2 = 1 3 , B 2 = 2 3 . Then, C 2 is equal to

$ aligned & A + B + C =180^ (Angle sum property of a triangle) \\ & A + B =180^ - C \\ & A+B 2 =90^ - C 2 \\ & ( A 2 + B 2 )= (90^ - C 2 ) \\ & A / 2+ B / 2 1- A / 2 B / 2 = C / 2 \\ & 1 3 + 2 3 1- 1 3 2 3 = C / 2 1 1- 2 9 = C / 2 \\ & 9 7 = C / 2 C / 2=7 / 9 aligned $

Question 1

Let A, B and C are the angles of a triangle and A 2 = 1 3 , B 2 = 2 3 . Then, C 2 is equal to

Accepted Answer

$ aligned & A + B + C =180^ (Angle sum property of a triangle) \ & A + B =180^ - C \ & A+B 2 =90^ - C 2 \ & ( A 2 + B 2 )= (90^ - C 2 ) \ & A / 2+ B / 2 1- A / 2 B / 2 = C / 2 \ & 1 3 + 2 3 1- 1 3 2 3 = C / 2 1 1- 2 9 = C / 2 \ & 9 7 = C / 2 C / 2=7 / 9 aligned $

Question 2

The sum of all values of x in [0,2 ], for which x+ 2 x+ 3 x+ 4 x=0, is equal to :

Accepted Answer

( x+ 4 x)+( 2 x+ 3 x)=0 2 5 x 2 3 x 2 +2 5 x 2 x 2 =0 2 5 x 2 \ 3 x 2 + x 2 \ =0 2 5 x 2 \ 2 x x 2 \ =0 2 5 x 2 =0 5 x 2 =0, , 2 , 3 , 4 , 5 , x=0, 2 5 , 4 5 , 6 5 , 8 5 , 2 x 2 =0 x 2 = 2 x= ; x=0 x= 2 , 3 2 So, sum =6 + +2 =9

Trigonometric Ratios & Identities — Previous Year Questions & Solutions