Question

Cos²θ(1+tan²θ) is equal to

a) Cos⁴ θ

b) cos θ

c) Cos²θ/Sinθ

d) 1


plz answer fast..and correct ​

Answer 1

Answer :-

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Given ,

sinθ + sin²θ = 1

To find ,

The value of : cos²θ + cos⁴θ

Now ,

sinθ + sin²θ = 1

sinθ = 1 - sin²θ

sinθ = cos²θ ---------- ( i )

[ • As sin²θ + cos²θ = 1

So , sin²θ = 1 - cos²θ ]

★ Method - 1

sinθ = cos²θ

( sinθ )² = ( cos²θ )²

sin²θ = cos⁴θ

1 - cos²θ = cos⁴θ

cos⁴θ + cos²θ = 1 [ ★ Required answer ]

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★ Method - 2

cos²θ + cos⁴θ

= sinθ + ( sinθ )²

[ • Putting the value of cos²θ = sinθ ]

= sinθ + sin²θ

= 1 [ • Given , sinθ + sin²θ = 1 ]

• So finally ,

[ cos²θ + cos⁴θ = 1 ]

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★ Be Brainly ★

Answer 2

Step-by-step explanation:

Tanθ+sinθ=m and tanθ-sinθ=n

∴, m²-n²

=(m+n)(m-n)

=(tanθ+sinθ+tanθ-sinθ)(tanθ+sinθ-tanθ+sinθ)

=(2tanθ)(2sinθ)

=4tanθsinθ

4√mn

=4√(tanθ+sinθ)(tanθ-sinθ)

=4√(tan²θ-sin²θ)

=4√{(sin²θ/cos²θ)-sin²θ}

=4√sin²θ{(1/cos²θ)-1}

=4sinθ√{(1-cos²θ)/cos²θ}

=4sinθ√(sin²θ/cos²θ)

=4sinθ√tan²θ

=4sinθtanθ

∴, LHS=RHS Hence Proved