Simplify - 4-1 - sin-2- nbsp-1 - tan-2-4-1-2-0-

The correct option is A 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 : 4(...

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