Question

Verify the following trigonometric identities.
sin x (cot x + tan x) = sec x

Answer 1

Step-by-step explanation:

LHS:cotx=cosx/sinx

tanx=sinx/cosx

sinx[(cos²x+sin²x)/sinxcosx]

=>sinx(1/sinxcosx)

=>1/cosx=>secx

hence proved.

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Answer 2

Step-by-step explanation:

Given that:Verify the following trigonometric identities.

sin x (cot x + tan x) = sec x

Solution:

We know that

$tan\:x=\frac{sin\:x}{cos\:x}\\\\cot\:x=\frac{cos\:x}{sin\:x}$

$sin\:x (cot\:x+tan\:x)=sec x\\\\sin\:x \bigg(\frac{cos\:x}{sin\:x}+\frac{sin\:x}{cos\:x}\bigg)$

Take LCM

$sin\:x \bigg(\frac{cos^2\:x+sin^2\:x}{sin\:x\:cos\:x}\bigg)$

$\because{cos^2\:x+sin^2\:x}=1$

$sin\:x \bigg(\frac{1}{sin\:x\:cos\:x}\bigg)\\\\=\frac{1}{cos\:x}\\\\=sec\:x$

LHS =RHS

Hence proved