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Question

If 5tanα = 4, show that 5sinα3cosα5sinα+2cosα=16

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Solution

We have,
5 tan αtanα=45
Now, 5sinα3cosα5sinα+2cosα
=5sinα3cosαcosα5sinα+2cosαcosα
=5sinαcosα3cosαcosα5sinαcosα+2cosαcosα
=5tan,α35tan,α+2
=5×4535×45+2
=434+2=16

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