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