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QUESTION: 1

Evaluate

Solution:

QUESTION: 2

Value of

Solution:

Since sin^{-1}(-π/2)=-sin^{-1}(π/2)=-1

so, cot ^{-1}(-1)

let (- cot^{-1}1)=α

cot α =-1 =cot (π/2+π/4) =3π/4

QUESTION: 3

The value of is given by

Solution:

QUESTION: 4

The principal value of tan^{-1} (-1) is given by

Solution:

QUESTION: 5

if 5 sin θ = 3, then is equal to

Solution:

sin θ is 3/5.

on simplifying:

(secθ + tanθ)/(secθ - tanθ)

We get, (1+sin θ)/(1-sin θ)

=(1+3/5)/(1-3/5)

=(8/2)

=4

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