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vekshin1
2 years ago
12

Prove each of these identities.

Mathematics
1 answer:
Stella [2.4K]2 years ago
8 0

Answer:

Identity (a) can be re-written as

sec x\ cosec x  - cot x = tan x

which we already proven in another question, while for idenity (b)

(A)\frac 1 {sin x} -sin x = cos x \frac{cos x}{sin x}\\\\(B)\frac {1-sin^2x}{sin x} = \frac {cos^2x} {sin x} \\\\(C) \frac {cos^2x}{sin x} =\frac {cos^2x} {sin x}

step A is simply expressing each function in terms of sine and cosine.

step B is adding the terms on the LHS while multiplying the one on RHS.

step C is replacing the term on the numerator with the equivalent from the pithagorean identity cos^2x  + sin^2x = 1

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