Question

Q1.51. If √1+sinx/√1-sinx = m, then the value of secx - tanx
equals
(1) m
(2) 1/m
(3) m²
(4) 1/m²​

Answer 1

Step-by-step explanation:

Answer:

$\begin{gathered}\implies \dfrac{\sqrt{1+sin\;x}}{\sqrt{1-sin\:x}} = m\\\\\\\text{Rationalising the given data, we get:}\\\\\\\implies \sqrt{\dfrac{(1+sin\;x)}{(1-sin\:x)} \times \dfrac{(1-sin\:x)}{(1-sin\:x)}}\\\\\\\implies \sqrt{\dfrac{1^2 - sin^2\:x}{(1-sin\:x)^2}} = m\\\\\\\implies \dfrac{cos\:x}{(1-sin\:x)} = m\\\\\\\text{Reciprocating the given data, we get:}\\\\\\\implies \dfrac{(1-sin\;x)}{cos\:x} = \dfrac{1}{m}\\\\\\\implies \dfrac{1}{cos\;x} - \dfrac{sin\:x}{cos\:x} = \dfrac{1}{m}\end{gathered}$

$\implies \boxed{\bf{sec\:x - tan\:x = m}}$

Hence Proved!!