SSC CGL 2024 PYQ — Question 65

The correct answer is Option 2 i.e. 1.

⇒ a sin³ X + b cos³ X = sin X cos X....(1)

⇒ a sin X = b cos X.....(2)

⇒ a sinX = b cos X

⇒ b = a sin X/cos X

⇒ b = a tan X.....(3)

On putting the value of b in Equation 1

⇒ a sin³ X + b cos³ X = sin X cos X

⇒ a sin³ X + (a tan X) cos³ X = sin X cos X

⇒ a sin³ X + (a sin X/cos X) cos³ X = sin X cos X  [tanA = sinA/cosA]

⇒ a sin³ X + (a sin X) cos² X = sin X cos X 

Given that x is neither 0° nor 90°

Now, divide both sides by sin X

⇒ a sin² X + a cos² X = cos X  [sin²A + cos²A = 1]

⇒ a = cos X

Put the value of a in eq 3

⇒ b = a tan X

⇒ b = cos X tan X

⇒ b = cos X × sin X/cos X

⇒ b = sin X

Now, we have the values of both and b So,

The value of a² + b² = cos²X + sin²X

⇒ a² + b² = 1 [sin²A + cos²A = 1]