Correct Answer - Option 3 : 1
Given:
sin6x + cos6x = p
sin4x + cos4x = q
Formula Used:
sin6x + cos6x = 1 – 3sin2xcos2x
sin4x + cos4x = 1 – 2sin2xcos2x
Calculation:
sin6x + cos6x = p
sin4x + cos4x = q
According to formulas –
p = 1 – 3sin2xcos2x
q = 1 – 2sin2xcos2x
According to question –
(3q – 2p) = (3 - 6sin2xcos2x – 2 + 6sin2xcos2x)
⇒ (3 – 2)
⇒ 1