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in Trigonometry by (53.3k points)

If tanθ = cotθ = a and sinθ +  cos θ = b, then solve (b2 - 1)2(a2  + 4).

1 Answer

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Best answer

Given that

tanθ - cotθ = a   ....(i)

and  sinθ  + cosθ .....(2)

Now,

Trick: Obviously the value of expression (b2 - 1)2 (a2 + 4) is independent of θ , therefore put any suitable value of θ. Let θ = 45° . We get a = 0, b = 2 so that [√2]2  - 1]2(02 + 4) = 4 .

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