Need help with solving trig equations and trig identities

1) 1 + sinx = cosx where -180 < x < 180 (Provide the general and particular solutions)

2) Prove

(cosx/2 - sinx/2)^2 = 1 - sinx

3) Prove

sin2A = 1 - 2sin^2 (45 - A)

2. expand and use cos^2+sin^2 = 1. Use sin2x = 2sinxcosx identity.

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Originally Posted by portage

1) 1 + sinx = cosx where -180 < x < 180 (Provide the general and particular solutions)

square both sides, change cos²x to 1 - sin²x, and solve the resulting quadratic in sinx ... don't forget to check for extraneous solutions


2) Prove

(cosx/2 - sinx/2)^2 = 1 - sinx

square the left side, then use the Pythagorean identity and the double angle identity for sine


3) Prove

sin2A = 1 - 2sin^2 (45 - A)

use the difference identity for sine to find sin(45-A) , square the result, then use the double angle identity for sine.

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