Question

Sin theeta -cos theeta =0 then
Sin ^4 theeta +cos ^4 theeta+tan^2 theeta =?

Answer 1

Answer:

3/2

Step-by-step explanation:

Sinθ - Cosθ = 0

Sinθ = Cosθ

This can happen only when θ = 45°.

Now Sin⁴θ + Cos⁴θ + Tan²θ

=  Sin⁴45° + Cos⁴45° + Tan²45°

= 1/4 + 1/4 + 1

= 3/2.

Answer 2

Answer:

let theeta=¤

so sin^4 ¤.+cos^4 ¤+tan^2 ¤ =3/2=1.5

Step-by-step explanation:

as given

sin¤--cos¤=0

then ,sin¤=cos¤

also sin¤ =sin (π/2--¤)

as we know.,

$\sin(\pi \div 2 - \alpha = \cos( \alpha ) )$

on cancelling sin terms from both sides .,

we get ,

¤=π/2--¤

2¤ =π/2

therfore ,,

¤ =π/2*1/2

¤=π/4

to prove:

cos .^4 ¤+sin^4 ¤+tan^2 ¤=0

so taking LHS. and putting the value of ¤ ,,

(cosπ/4)^4+(sinπ/4)^4+(tanπ/2)^2

=

(1/√2)^4+(1/√2)^4+(1)^2

=

$\frac{1}{4} + \frac{1}{4 } + 1$

=

$\frac{1 + 1 + 4}{4}$

=

$\frac{6}{4} = \frac{3}{2 } = 1.5$