Question

hey
please solve vi and. viii​

Answer 1

Answer:

Question: viii

To prove;

(sinA + cosecA)^2 + (cosA + secA)^2

= 7 + (tanA)^2 + (cotA)^2

Proof:

LHS=(sinA+cosecA)^2 + (cosA+secA)^2 = (sinA)^2+(cosecA)^2 + 2sinA•cosecA

+(cosA)^2 + (secA)^2 + 2cosA•secA

= (sinA)^2 + (cosecA)^2 + 2sinA(1/sinA)

+(cosA)^2 + (secA)^2 + 2cosA(1/cosA)

= (sinA)^2 + (cosecA)^2 + 2 + (cosA)^2

+ (secA)^2 + 2

= {(sinA)^2 + (cosA)^2} + (cosecA)^2

+ (secA)^2 + 4

= 1 + {(cotA)^2 + 1} + {(tanA)^2 + 1} + 4

= 7 + (tanA)^2 + (cotA)^2

= RHS.

Hence proved.

For question:vi, refer to the attachment