Precalc - trig identities. decent explanation, .

12. Recall the half-angle identity,

where we take the positive square root because is an angle in a right triangle, which means , so . For such an angle, it's always the case that .

Use the Pythagorean theorem to find the length of the hypotenuse:

Then

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13. is in quadrant II, which means , so . In other words, is in quadrant I, so . From the half-angle identity we get

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14. Simplification follows from the definitions of each function:

So we have

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15. Use the Pythagorean identity:

Then

c

step-by-step explanation: