If 1-tan x- x1- x-cosec x-2 a- the value of a is-

The correct option is A 1(1+tan x+sec x)(1+cot x cosec x) =(1+ sin x/cos x+ 1/cos x)(1+cos x/sin x+ 1/sin x) =(cos x +sin x+1/cos x)(sin x+cos x 1/sin x) = [(c ...

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Standard X

Mathematics

Trigonometric Identities

If 1+tan x+ x...

Question

If (1 + tan x + sec x)(1 + cot x - cosec x) = 2a, the value of a is:

0.0

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Solution

The correct option is B 1
$(1 + t a n x + s e c x) (1 + c o t x - c o s e c x)$
$= (1 + \frac{s i n x}{c o s x} + \frac{1}{c o s x}) (1 + \frac{c o s x}{s i n x} + \frac{- 1}{s i n x})$
$= (\frac{c o s x + s i n x + 1}{c o s x}) (\frac{s i n x + c o s x - 1}{s i n x})$
$= [\frac{(c o s x + s i n x) + 1}{c o s x}] [\frac{(s i n x + c o s x) - 1}{s i n x}]$
$= \frac{(c o s x + s i n x)^{2} - 1^{2}}{(c o s x) (s i n x)}$
$= \frac{c o s^{2} x + s i n^{2} x + 2 (c o s x) (s i n x) - 1}{(c o s x) (s i n x)}$
$= \frac{1 + 2 (c o s x) (s i n x) - 1}{(c o s x) (s i n x)} [S i n c e c o s^{2} x + s i n^{2} x = 1]$
= 2

Given that $(1 + t a n x + s e c x) (1 + c o t x - c o s e c x) = 2 α,$ we have:
$2 α = 2 \Rightarrow α = 1$

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