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Question

If m sin θ=n cos θ, then show that:

tan θ+cot θtan θcot θ=n sin θ+m cos θn sin θm cos θ=n2+m2n2m2 [4 MARKS]

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Solution

Solution: 2 Marks each

(a)tan θ+cot θtan θcot θ=nm+mnnmmn

=n2+m2mnn2m2mn

=n2+m2n2m2.......(1)


(b)n sin θ+m cos θn sin θm cos θ

÷cos θ

n tan θ+mn tan θ+m

=n(nm)+mn(nm)m

=n2+m2mn2m2m

=n2+m2n2m2.......(2)

From (1) and (2)

tan θ+cot θtan θcot θ=n sin θ+m cos θn sin θm cos θ=n2+m2n2m2

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