1.

If tan² θ = 1 – e², then the value of sec θ + tan³ θ × cosec θ is

Answer»

GIVEN:- tan²θ = 1 - e²

We know:- 1 + tan²θ = sec²θ , sin²θ + cos²θ = 1

now, sec²θ = 1 + tan²θ

=> sec ²θ = 1 + (1 - e²)

=> sec²θ = 2 - e²

=> secθ = (2 - e²)½

so, secθ + tan³θ . cosecθ

=> 1/cosθ + sin³θ/cos³θ . 1/sinθ

=> (cos²θ + sin²)/cos³θ

=> 1/cos³θ

=> sec³θ = (2 - e²)^3/2


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