Question

If cosα = 12/13 show that sinα(1-tanα) = 35/156

Answer 1

Step-by-step explanation:

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Answer 2

cos θ =12/13= B/H

By applying Pythagoras theorem

H²= B²+P²

13²= 12²+P²

169= 144+P²

169-144=P²

25=P²

P²=25

P= 5

sinθ=P/H=5/13

tanθ= P/B= 5/12

Now

sinθ(1-tanθ)=35/156

LHS

5/13(1-5/12)

5/13(7/12)

35/156= RHS

Hence proved

Note: B=Base,P=Perpendicular and H=Hypotenuse