Question

What is the value of cos^2θ – sin^2θ if the length of the opposite side is 20 units and the length of the hypotenuse is 29 units?

(a) \(\frac {- 41}{841}\)

(b) \(\frac {- 41}{840}\)

(c) \(\frac {41}{841}\)

(d) \(\frac {41}{840}\)

I have been asked this question in an interview.

The question is from Trigonometric Ratios topic in portion Trigonometry of Mathematics – Class 10

Answer 1

Correct choice is (a) \(\frac {- 41}{841}\)

The best explanation: From Pythagoras theorem, (Hypotenuse)^2 = (Opposite side)^2 + (Adjacent side)^2

(Adjacent side)^2 = (Hypotenuse)^2 – (Opposite side)^2

Adjacent side = √441 = 21

Cosθ = \(\frac {Length \, of \, the \, adjacent \, side}{Length \, of \, the \, hypotenuse} = \frac {21}{29}\), Sinθ = \(\frac {Length \, of \, the \, opposite \, side}{Length \, of \, the \, hypotenuse} = \frac {20}{29} \)

cos^2θ – sin^2θ = (\(\frac {21}{29}\))^2 + (\(\frac {20}{29} \))^2

= \(\frac {- 41}{841}\)