Question

If tan θ=3/4, then $cos^{2}\Theta-sin^{2}\Theta$=
(a) $\frac{7}{25}$
(b) 1
(c)$\frac{-7}{25}$
(d) $\frac{4}{2}$

Answer 1

SOLUTION :  

The correct option is (a) : 7/25

Given : tan θ  = ¾  

In right angle ∆ ,  

tan θ =  perpendicular/base = 3/4

perpendicular = 3 , base = 4

Hypotenuse = √( perpendicular)² + (Base)²

[By Pythagoras theorem]

Hypotenuse = √ 3² + 4² = √9 + 16 = √25

Hypotenuse = √25 = 5  

Hypotenuse = 5

sin θ = perpendicular / hypotenuse  = 3/5

cos θ = base/ hypotenuse = 4/5

The value of : (cos²θ - sin² θ )

= [(⅘)² - (⅗)²]

=( 16/25 - 9 /25)

= [(16 - 9)/25

= 7/25

cos²θ - sin² θ = 7/25

Hence, the value of cos²θ - sin² θ = 7/25

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

The correct option is a. 7/25