Question

what does tanx sinx (cos^2x cscx- sinx) simplify to

Answer 1

Answer:

Tan x cos(2x)

Step-by-step explanation:

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Answer 2

The expression tan x sin x($cos^{2} x$ cosec x-sin x) is equal to - tan x+sin2x.

What are trigonometric ratios?

Trigonometric ratios are the ratios of the sides of right angled triangle. Sin, cos, tan, cosec, sec, cot are the trigonometric ratios. Sin is the ratio of perpendicular to hypotenuse, cos is the ratio of base and hypotenuse, tan is the ratio of perpendicular and base, cosec is ratio of hypotenuse and perpendicular, secant is the ratio of hypotenuse and base, cotangent is the ratio of base and perpendicular.

How to simplify expression?

The expression is given as tan x sin x($cos^{2} x$ cosec x-sin x)

=tan x sin x $cos^{2} x cosecx$-sin x sin x tan x

=tan x sin x $cos^{2}x$ /sin x-$sin^{2}x$ tan x

=tan x *cos x* cos x- $sin^{2} x$ tan x

=-tan x ($sin^{2}x -cos^{2} x$)

=-tan x(1-$cos^{2} x$-$cos^{2} x$)        ($sin^{2}x +cos^{2} x=1$)

=-tan x(1-2$cos^{2} x$)

=-tan x+2 tan x $cos^{2}x$

=-tan x +2sinx/ cos x *$cos^{2} x$     (tan x= sin x/ cos x)

=-tanx+2 sin x cos x

=-tan x+ sin 2x       (Sin 2x= 2 sin x cos x)

Hence the expression tan x sin x ($cos^{2} x$ cosec x-sin x) is -tan x+ sin2x.

Learn more about trigonometric ratios at https://brainly.com/question/24349828

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