Question
Prove the identity
sin(90°x) + sin(90° - x) = 2 cos x
We begin on the left side of the equation by using Sum and Difference Formulas. We can then combine like terms,
find all exact values, and simplify
(ar
= (sin 90° cos x + cos 90° sin x) +
sin(90°x) + sin(90° - x)
sin
O
COS X Cos 90° sin x
o
COS X
= 2 sin
= 2
COS X
= 2 cos x

Image Transcription

Prove the identity sin(90°x) + sin(90° - x) = 2 cos x We begin on the left side of the equation by using Sum and Difference Formulas. We can then combine like terms, find all exact values, and simplify (ar = (sin 90° cos x + cos 90° sin x) + sin(90°x) + sin(90° - x) sin O COS X Cos 90° sin x o COS X = 2 sin = 2 COS X = 2 cos x

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MathTrigonometry

Trigonometric Ratios