`(1+tan^(2)v)(1-sin v)(1+sin v)=1`

Find the principal values of the following (i) sin^(-1) (sin 1) (ii) sin^(-1) (sin 2) (iii) sin^(-1) (sin 10) (iv) sin^(-1) (sin 20) (v) sin^(-1) (sin 100) (vi) sin^(-1) (sin. (29 pi)/(5))

tan (45 ^ (@) + (A) / (2)) = sqrt ((1 + sin A) / (1-sin A)) = sec A + tan A

Prove: (1+tan^(2)A)+(1+(1)/(tan^(2)A))=(1)/(sin^(2)A-sin^(4)A)

tan^(-1) 1 + sin^(-1)(-1/2)

If sin^(4)A+sin^(2)A=1 then prove that (1)/(tan^(4)A)+(1)/(tan^(2)A)=1

" (v) "int(cosx)/(1+sin x)dx

(1-2sin^(2)alpha)/(1+sin2 alpha)=(1-tan alpha)/(1+tan alpha)

prove that :(1-sin2 theta)/(1+sin2 theta)=((1-tan theta)/(1+tan theta))^(2)

(1-2sin^(2)alpha)/(1+sin2 alpha)=(1-tan alpha)/(1+tan alpha)

int((1+v)/(1-v))dv