SSC CPO 2022 PYQ — Question 105

The correct answer is option 1 i.e. 7.

If cos A = sin² A and a sin¹² A + b sin¹⁰A + c sin⁸ A + sin⁶ A = 1

cos A = sin² A 

Squaring both sides

cos² A = sin⁴ A 

1 - sin² A = sin⁴ A 

sin⁴ A +  sin² A = 1

Cubing on both sides

sin¹² A + 3 sin¹⁰A + 3 sin⁸ A + sin⁶ A = 1

On comparing by this equation

a sin¹² A + b sin¹⁰A + c sin⁸ A + sin⁶ A = 1

a = 1, b = 3 , c = 3

then a + b + c = 7