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Question
If tanθ = 1 then, find the value of
`(sinθ + cosθ)/(secθ + cosecθ)`
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Solution
tanθ = 1 ...(Given)
We know that, tan45° = 1
∴ θ = 45º
Now,
sinθ = sin 45º = `1/sqrt2`
cosθ = cos 45º = `1/sqrt2`
secθ = sec 45º = `sqrt2`
cosecθ = cosec 45º = `sqrt2`
∴ `(sinθ + cosθ)/(secθ + cosecθ)`
⇒ `(1/sqrt2 + 1/sqrt2)/(sqrt2 + sqrt2)`
⇒ `(2/sqrt2)/(2sqrt2)`
⇒ `cancel2/sqrt2 × 1/(cancel2sqrt2)`
⇒ `1/2`
∴ `(sinθ + cosθ)/(secθ + cosecθ) = 1/2`
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