SOLUTION: Express cos 90- cos 50 as a product containing only sines and/or cosines

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Question 1010813: Express cos 90- cos 50 as a product containing only sines and/or cosines
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52790) (Show Source):
You can put this solution on YOUR website!
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Express cos(90�)- cos(50�) as a product containing only sines and/or cosines
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Use this formula of Trigonometry

(see the lesson Addition and subtraction of trigonometric functions in this site).

When you apply it, you will get

cos(90�)- cos(50�) = -2*sin((140�)/2)*sin((40�)/2) = -2*sin(70�)*sin(20�).

Answer by MathTherapy(10552) (Show Source):
You can put this solution on YOUR website!

Express cos 90- cos 50 as a product containing only sines and/or cosines

Difference of two angles formula: cos (A - B) = cos A cos B + sin A sin B
cos (90 - 50) = cos 90 cos 50 + sin 90 sin 50
cos (90 - 50) = 0 * cos 50 + 1 * sin 50
cos (90 - 50) = 0 + sin 50

OR
Shortcut
sin and cos are COFUNCTIONS, so cos (90 - 50) = cos 40 = sin (90 - 40), or sin 50