Trigonometry

The complementary angle of 45° 45′ is ______.

A. 45° 55′

B. 44° 25′

C. 44° 15′

D. 46° 25′

The sides a, b, c (taken in order) of a ΔABC are in A.P. If \(\rm \cos \alpha =\frac{a}{b+c}\), \(\rm \cos \beta =\frac{b}{c+a}\), \(\rm \cos \gamma =\frac{c}{a+b}\), then \(\rm \tan^{2}\frac{\alpha }{2}+\tan^{2}\dfrac{\gamma }{2}\) is equal to:

[Note: All symbols used have usual meanings in triangle ΔABC.]

Consider the following for real numbers α, β, γ and δ:

1. sec α = 1/5

2. tan β = 15

3. cosec γ = 1/3

4. cos δ = 4