Consider a triangle $P Q R$ , right angled at $P$ , in which $P Q = 21$ units, $Q R = 29$ units and $∠ P Q R = θ$ , then find the value of $\cos^{2} θ - \sin^{2} θ$

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$\frac{- 41}{841}$

$\frac{41}{841}$

$- 1$

answer is A.

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Detailed Solution

In $P Q R$ , we have $P R = \sqrt{Q R^{2} - P Q^{2}} = \sqrt{{(29)}^{2} - {(21)}^{2}} = \sqrt{400} = 20$

$\sin θ = \frac{20}{29}$

$\cos θ = \frac{21}{29}$

$\cos^{2} θ - \sin^{2} θ = {(\frac{20}{29})}^{2} - {(\frac{21}{29})}^{2} = \frac{- 41}{841}$

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