Question

P.T 1+secФ/secФ=sin²Ф/1-cosФ

Answer 1

LHS
1+secФ/secФ⇒1/secФ+secФ/secФ⇒cosФ+1
RHS
sin²Ф/1-cosФ⇒1-cos²Ф/1-cosФ        using sin²Ф+cos²Ф=1
(1-cosФ) (1+cosФ)/1-cosФ              using a²-b²=(a-b) (a+b)
cosФ+1
LHS=RHS
Hence proved

Answer 2

LHS = $\frac{1+sec teta}{secteta}$

=$\frac{1}{secteta} + \frac{secteta}{secteta}$

= cosФ+1


RHS = $\frac{ 1-\cos^{2}teta }{1-costeta}$

=$\frac{(1-costeta)(1+costeta)}{1-costeta}$

=cosФ+1

LHS=RHA
Hence Proved.