Question

If \[\tan \theta = \frac{3}{4}\]  then cos² θ − sin² θ = 

Options

• \[\frac{7}{25}\]

•  1

• \[\frac{- 7}{25}\]

• \[\frac{4}{25}\]

Answer 1

Given that:` tan θ=3/4` 

Since ` tan x= "Perpendicular"/"Base"` 

⇒` "Perpendicular"=3` 

⇒`"Base"=4` 

⇒ `"Hypotenuse"=sert(9+16)` 

⇒` "Hypotenuse"=5` 

We know that  sin θ= `"Prependicular"/"Hypotenuse" and cos θ= "Base"/"Hypotenuse" `

We find: 

`cos^2θ-sin ^2 θ`

=`(4/5)^2-(3/5)^2` 

=`16/25-9/25` 

= `7/25`