Question

Theta is acute and alpha is obtuse . It is known that sin theta=2/5 and cosec alpha =2. Compute the exact values of
a) sec theta
b) cos alpha
c) tan( theta + alpha)

Answer 1

I will use θ for theta, and a for alpha
sin θ = 2/5 , so θ must be in quadrant I
cosec a =2 , so sin a = 1/2, but a is to be obtuse, so a is in II

if sinθ = 2/5 , using a right-angled triangle, cosθ = √21/5, and secθ = 5/√21
if sin a = 1/2, then cos a = √3/2
tan(θ+a) = sin(θ+a) / cos(θ+a)
use the expansion for sin(A+B) and cos(A+B) to find the numerator and denominator
of the right side, then evaluate.

Answer 2

Thanks much