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Please explain in detail the following:

Please explain step by step how to complete the following:

In the following determine graphically whether the equation could possibly be an identity. If it could, prove that it is.

5. sin^4 t - cos^4 t = 2 sin² t -1

ans. - sin^4t - cos^4 t = (sin²2t - cos²t) (sin²t + cos²t) = (sin²t-(1-sin²t)) (1) =
2 sin²t - 1

6. 1 + 2 cos²t + cos^4t = sin^4t

ans.?

7. sint/1-cost = 1+cost/sint

ans. sint/1-cost = sint/1-cost*(1+cost)/(1+cost) = sin t (1 + cos t)/1-cos²t =
sint (1+cost)/sin²t = 1+cost/sint

11. (sinx + cos x)² - sin2x = 1

Solution Preview

5. sin^4 t - cos^4 t = 2 sin² t -1
It is true.
First, we use the formula a^2-b^2=(a+b)(a-b), then
sin^4t-cos^4t=(sin^2t)^2-(cos^2t)^2=(sin^2t+cos^2t)(sin^2t-cos^2t)
Second, we use the formula ...

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