`(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))

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))

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

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

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

If u = tan^(-1) (( sqrt(1- x^(2) ) - 1)/( x) ) and v = sin^(-1) x , then (du)/(dv) is equal to a) sqrt( 1- x^2) b) - (1)/(2) c)1 d)-x

(v) tan^(-1)sqrt((1+cos x)/(1-cos x))

If u = (1 + cos theta) (1+ cos2 theta) - sin theta sin 2theta, v = sin theta (1 + cos2 theta) + sin 2 theta(1 + cos theta), "show that" u^(2) + v^(2) = 4(1 + cos theta) (1 + cos 2theta).