Question

$(1 - sin^2 \: theta)(1 + tan^2 \: theta)$
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Answer 1

Given to find the value of :-

(1 - sin²θ)(1+ tan²θ)

SOLUTION:-

We can find this Solution very easily by Trigonometric identities

As all we know that,

sin²θ + cos²θ = 1

1 - sin²θ = cos²θ _______ 1

sec²θ - tan²θ = 1

sec²θ = 1+tan²θ_________ 2

(1 - sin²θ)(1+ tan²θ)

= cos²θ × sec²θ

From trigonometric relations

secθ = 1/cosθ

= cos²θ × 1/cos²θ

= 1

So, (1 - sin²θ)(1+ tan²θ) = 1

Know more :-

Trigonometric Identities

sin²θ + cos²θ = 1

sec²θ - tan²θ = 1

csc²θ - cot²θ = 1

Trigonometric relations

sinθ = 1/cscθ

cosθ = 1 /secθ

tanθ = 1/cotθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

Trigonometric ratios

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

cotθ = adj/opp

cscθ = hyp/opp

secθ = hyp/adj