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The value of sin x (cosec x – sin x)(tan x + cot x) is –

The value of sin x (cosec x – sin x)(tan x + cot x) is – Correct Answer cot x

GIVEN:

sin x (cosec x – sin x)(tan x + cot x)

FORMULA USED:

sin2x + cos2x = 1

CALCULATION:

⇒ sin x (cosec x – sin x)(tan x + cot x)

⇒ sin x (1/sin x – sin x)(sin x/cos x + cos x/sin x)

⇒ sin x (1 – sin2x)/sin x × (sin2x + cos2x)/(sin x cos x)

⇒ cos2x × 1/(sin x cos x)

⇒ cos x/sin x

⇒ cot x

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