Question

if tan²θ=1-e² ,then the value of secθ+tan³θ∘cosecθis​

Answer 1

Answer:

(2-e²)^3/2

Step-by-step explanation:

Given,

tan² theta = 1 - e² .....................(I)

We know,

sec² theta= 1+ tan² theta ..........(II)

Putting the value of equation(I) in equation(II),

sec² theta = 1+(1-e²) = 2-e² ..........(III)

sec theta = √(2-e²) ........................(IV)

To find : sec theta + tan³ theta.cosec theta=?

=sec theta + tan³ theta.cosec theta

=sec theta + (tan² theta.tan theta).cosec theta

=sec theta + tan² theta.(tan theta.cosec theta)

= sec theta + tan² theta. (sec theta)

= sec theta.(1+tan² theta)

= sec theta.sec² theta

Putting the values from (III) and (IV),

= (2-e²)^1/2 . (2-e²)

= (2-e²)^3/2