Question 70

If θ is acute angle and tanθ - cotθ = 0, then what is the value of $$tan^{26}θ + cot^{100}θ$$ ?

Solution

Given : $$tan\theta-cot\theta=0$$

=> $$tan\theta=cot\theta$$

=> $$tan\theta=\frac{1}{tan\theta}$$

=> $$tan^2\theta=1$$

=> $$tan\theta=\sqrt1=1$$

=> $$\theta=tan^{-1}(1)=45^\circ$$

To find : $$tan^{26}θ + cot^{100}θ$$

= $$tan^{26}(45^\circ)+cot^{100}(45^\circ)$$

= $$1+1=2$$

=> Ans - (D)

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