Question 71

The value of tan80° tan10° + $$sin^2$$70° + $$sin^2$$20° is

Solution

Expression : $$tan(80^\circ)tan(10^\circ)+sin^2(70^\circ)+sin^2(20^\circ)$$

= $$tan(80^\circ)tan(90^\circ-80^\circ)+sin^2(70^\circ)+sin^2(90^\circ-70^\circ)$$

Using, $$tan(90^\circ-\theta)=cot\theta$$ and $$sin(90^\circ-\theta)=cos\theta$$

= $$tan(80^\circ)cot(80^\circ)+sin^2(70^\circ)+cos^2(70^\circ)$$

Using, $$(sin^2\theta+cos^2\theta=1)$$ and $$tan\theta cot\theta=1$$

= $$1+1=2$$

=> Ans - (C)

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