Q)  If sin α = 1/√2 and cot β = √3, then find the value of cosec α + cosec β.

Ans:   Given that, sin α =  1/√2

⇒ cosec α = 1 / sin α

= 1/ (1/√2)

⇒ cosec α = √2 …………(i)

Next, we have value of cot β and need to arrive at cosec β

We know that 1 + cot ² β = cosec ² β

⇒ cosec β = √ (1 + cot ² β)

Let’s put cot β = √3 in above relation:

⇒ cosec β = √ (1 + cot ² β)

= √ (1+ (√3)²) = √ (1 + 3)

⇒ cosec β = 2 …………… (ii)

Next, let’s find out value of cosec α + cosec β

=   √2  + 2 [from equations (i) and (ii)]

= √2 (1+√2)

Therefore value of cosec α + cosec β = √2 (1+√2).

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