Mathematics
If cos x = cos 40° sin 50° + sin 40° cos 50°, then find the value of angle x.
Trigonometric Identities
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Answer
Given:
cos x = cos 40° sin 50° + sin 40° cos 50°
⇒ cos x = cos (90° - 50°) sin 50° + sin (90° - 50°) cos 50°
⇒ cos x = sin 50° sin 50° + cos 50° cos 50°
⇒ cos x = sin2 50° + cos2 50°
⇒ cos x = 1
⇒ cos x = cos 0°
Hence, x = 0°.
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