Question

If sin theta equal to a upon b find sec theta + tan theta in terms of a and b

Answer 1

Given sin theta = a/b
sec theta + tan theta 
1/cos theta + sin theta/cos theta
(1+sin)/cos
[cos in terms of sin is sqrt(1-sin^2theta) ]
(1+sin)/sqrt(1-sin^2theta)
(1+a/b)/[sqrt(1 - (a/b)^2)]
(b+a/b)/[sqrt(b^2-a^2/b^2)]
(b+a/b)/[sqrt(b^2-a^2)/sqrt(b^2)]
(b+a/b)/[sqrt(b^2-a^2)/b]
b+a/sqrt(b^2-a^2)

Answer 2

given
sin θ = a/b ----(1)
i)cos θ = √1- sin²θ
= √1- (a²/b²)
=√(b² - a²) / b
ii) sec θ + tan θ
=1/cos θ + sin θ/ cos θ

= 1/ [√b² -a²]/b + (a/b)/[√(b²-a²)/b]

=b/√(b²-a²) + a/√(b² -a²)

= (b+a)/ √(b²-a²)