Question

if tan theta is equal to 2 by 3 then find the value of sin square theta + cos square theta

Answer 1

HELLO DEAR,

GIVEN THAT:- tan∅ = 2/3

And we have to find the value of sin²∅ + cos²∅ = ?

it does not deepend on the value of tan∅

Simply,we know this is a identity (sin²∅ + cos²∅) = 1

If we want to finding the value of sin²∅ + cos²∅

So, tan∅ = 2/3 = height/base

Hypotenuse² = 2² + 3²

H = √13

So, sin∅ = height/hypotenuse = 2/√13
sin²∅ = 4/13------------( 1 )

cos∅ = base/hypotenuse = 3/√13
cos²∅ = 9/13----------( 2 )

Adding----------( 1 ) &---------( 2 )

we get,

sin²∅ + cos²∅ = 4/13 + 9/13

sin²∅ + cos²∅ = 13/13 = 1

HENCE, sin²∅ + cos²∅ = 1


I HOPE ITS HELP YOU DEAR,
THANKS