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Question
Evaluate the following :
(sin 72° + cos 18°) (sin 72° − cos 18°)
Solution
We have to find: (sin 72° + cos 18°) (sin 72° − cos 18°)
Since `sin(90^@ - theta) = cos theta` So
sin 72° + cos 18°) (sin 72° − cos 18°) = `(sin 72^@)^2 - (cos 18^@)^2`
`= [sin (90^@ - 18^@)]^2 - (cos 18^@)^2`
`= (cos 18^@)^2 - (cos 18^@)^2`
`= cos^2 18^@ - cos^2 18^@`
= 0
So value of `(sin 72^@ + cos 18^@)(sin 72^@ - cos 18^@)` is 0
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