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Question
If \[\cos \theta = \frac{2}{3}\] then 2 sec2 θ + 2 tan2 θ − 7 is equal to
Options
1
0
3
4
Solution
Given that: `cos θ=2/3`
We have to find `2 sec^2 c+2 tan ^2 θ-7`
As we are given
`cos θ=2/3`
⇒ `"Base"=2`
⇒ `"Hypotenuse"=3`
⇒ `"Perpendicular"= sqrt((3)^2-(2)^2)`
⇒`"Perpendicular"=sqrt5`
We know that:
`cos θ="Base"/"Hypotenuse"`
`tan θ= "Perpendicular"/"Base"`
Now we have to find:` 2 sec^2θ+2 tan^2 θ-7.` so
`2 sec^2θ+2 tan ^2 θ-7`
=`2(3/2)^2+2(sqrt5/2)^2-7`
= `18/4+10/4-7`
=`(18+10-28)/4`
= 0
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