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how to simplify trig identities

Sagot :

LammettHash

cos(x) (tan(x) + cot(x))

Recall that tan(x) = sin(x)/cos(x) and cot(x) = 1/tan(x) = cos(x)/sin(x). Then

cos(x) (sin(x)/cos(x) + cos(x)/sin(x)) = sin(x) + cos²(x)/sin(x)

Write both terms with a common denominator and combine the fractions:

sin²(x)/sin(x) + cos²(x)/sin(x) = (sin²(x) + cos²(x))/sin(x)

Recall the Pythagorean identity,

sin²(x) + cos²(x) = 1

so our expression reduces to

1/sin(x)

Finally, recall that csc(x) = 1/sin(x) and we're done. So

cos(x) (tan(x) + cot(x)) = csc(x)

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