Question

if cosA=tanA then find cosecA and tanA×cosA
note: first answer will be made as brainliest, rated 5⭐,thanked,and then i will follow u.​

Answer 1

cos C=tan A

so tan C=sqrt(1-tan ^2 A)/tan A

cos B=tan C=sqrt(1-tan ^2 A)/tan A

so tan B=sqrt((2×tan ^2 A-1)/(1-tan ^2 A))

But cos A=tan B

cos A=sqrt(2×tan ^2 A-1)/(1-tan ^2 A))

cos ^2 A=(2×tan ^2 A-1)/(1-tan ^2 A)

1/sec ^2 A=(2×tan ^2 A-1)/(1-tan ^2 A)

1/(1+tan ^2 A)=(2×tan ^2 A-1)/(1-tan ^2 A)

tan ^4 A +tan ^2 A -1=0

tan ^2 A=(-1+√5)/2

cot ^2 A=2/(√5 -1)

cosec ^2 A -1 =2/(√5 -1)

cosec ^2 A=(1+√5)/(√5 -1)

sin ^2 A=(√5–1)/(√5+1)=(√5–1)^2/(√5+1)(√5–1)

sin ^2 A=((√5–1)^2)/4

sin A=(√5–1)/2.

MARK ME BRAINLIEST ^_^