Simplify -41-sin 2-1-tan 2-

The correct option is C 4 Using the identity, 1 sin^2θ = nbsp;cos^2θ and 1 + nbsp;tan^2θ = nbsp;sec^2θ We have, 4(1 – sin^2θ) nbsp;(1 + tan^2θ) nb ...

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Standard X

Mathematics

Trigonometric Identities

Simplify :41-...

Question

Simplify :
4(1 – $s i n^{2} θ$ ) (1 + $t a n^{2} θ$ )

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Solution

The correct option is A
4

Using the identity,
1 - $s i n^{2} θ$ = $c o s^{2} θ$ and
1 + $t a n^{2} θ$ = $s e c^{2} θ$

We have, 4(1 – $s i n^{2} θ$ ) (1 + $t a n^{2} θ$ )
$= 4 c o s^{2} θ \times s e c^{2} θ = 4 (∵ s e c θ = \frac{1}{c o s θ})$

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Similar questions

$4 (1 - {sin}^{2} θ) (1 + {tan}^{2} θ) =$

Choose the correct answer:

(1 - {sin}^{2} θ) (1 + {tan}^{2} θ) =

_____.

Q. Find the value of

{cos}^{2} θ (1 + {tan}^{2} θ) + {sin}^{2} θ (1 + {cot}^{2} θ)

Q. If

4 sin θ = 3 cos θ

, find

\frac{{sec}^{2} θ}{4 (1 - {tan}^{2} θ)}

(t a n^{2} θ + c o s^{2} θ + 2 t a n θ c o s θ)

simplifies to

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Simplify : 4(1 – sin2θ) (1 + tan2θ)

The correct option is A 4 Using the identity, 1 - sin2θ = cos2θ and 1 + tan2θ = sec2θ We have, 4(1 – sin2θ) (1 + tan2θ) =4 cos2θ×sec2θ=4 (∵sec θ=1cos θ)

Simplify :
4(1 – $s i n^{2} θ$ ) (1 + $t a n^{2} θ$ )

The correct option is A
4

Using the identity,
1 - $s i n^{2} θ$ = $c o s^{2} θ$ and
1 + $t a n^{2} θ$ = $s e c^{2} θ$

We have, 4(1 – $s i n^{2} θ$ ) (1 + $t a n^{2} θ$ )
$= 4 c o s^{2} θ \times s e c^{2} θ = 4 (∵ s e c θ = \frac{1}{c o s θ})$