Which of the following is an identity? A. secx tanx - cosx cotx = sinx B. (tanx + cotx)(sinx cosx) = 1 C. sin2x = 4 - 2cos2x D. cosx(2sinx + 1) = 0

letter B

(tanx + cotx)(sinxcosx) = 1
[(sinx/cosx) + (cosx/sinx)](sinxcosx) = 1
[(sinxcosx)(sinx/cosx) + (sinxcosx)(cosx/sinx)] = 1
[(sinx)^2 + (cosx)^2] = 1
*Pythagorean Identity*
1 = 1

Answer Link

MubeenaD MubeenaD · Answer 2 · 2022-06-01T11:09:15+02:00

Using trigonometry property, the best option is B.

What is trigonometry?

Trigonometry deals with "the relationship between the sides and the angles of triangles".

According to the question,

[tan x + cot x] (sin x + cos x) = 1

[tex][\frac{sin x}{cos x}+\frac{cos x}{sin x} ] (sin x cos x) = 1[/tex] [tan x = [tex]\frac{sin x}{cos x}[/tex] and cot x = [tex]\frac{cos x}{sin x}[/tex]]

[tex]\frac{sin x}{cos x} (sin x cos x) + \frac{cos x}{sin x}(sin x cos x) =1[/tex]

[tex]sin^{2}x +cos^{2}x = 1[/tex] [By cancellation law]

By the Pythagoras theorem, [tex]sin^{2}x +cos^{2}x = 1[/tex] .

Hence, using trigonometry property, the best option is B.

Learn more about trigonometry here

https://brainly.com/question/26719838

#SPJ2