Correct Answer - Option 2 : 22/23
Given:
tanx + cotx = 5
Formula Used:
sin6x + cos6x = 1 – 3sin2xcos2x
sin4x + cos4x = 1 – 2sin2xcos2x
tanx + cotx = cosecxsecx
Calculation:
tanx + cotx = 5
⇒ sinx/cosx + cosx/sinx = 5
⇒ (sin2x + cos2x)/sinxcosx = 5
⇒ 1/sinxcosx= 5
⇒ sinxcosx = 1/5
According to question –
(sin6x + cos6x)/ (sin4x + cos4x)
⇒ (1 – 3sin2xcos2x)/ (1 – 2sin2xcos2x)
⇒ (1 – 3/25)/ (1 – 2/25)
⇒ (22/25)/(23/25)
⇒ 22/23
∴ The correct answer is 22/23.