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Question
If \[\sin \theta = \frac{4}{5}\] what is the value of cotθ + cosecθ?
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Solution
Given: `sin θ=4/5`
We know that,
`sin^2 θ+cos^2=1`
⇒ `(4/5)^2+cos^2 θ=1`
⇒ `16/25+cos^2 θ=1`
⇒ `cos^2θ=1-16/25`
⇒`cos^2θ=9/25`
⇒`cosθ=3/5`
We have,
`cos θ+cosec θ=cosθ/sin θ+1/sinθ`
= `(3/5)/(4/5)+1/(4/5)`
= `3/4+5/4`
= `2`
Hence, the value of cotθ + cosecθ is 2.
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