Question:

If tan = 1 then, find the values of (sin+ cos)/( sec+ cosecθ ).

Answer:

Given tan = 1
We know that tan 45˚ = 1
= 45˚
sin 45 = 1/√2
cos45 = 1/√2
sec45 = √2
cosec45 = √2
(sin+ cos)/( sec+ cosecθ ) = (sin45+ cos45)/( sec45+ cosec45 )
= [(1/√2)+( 1/√2)]÷[√2+√2]
= (2/√2)÷2√2
= (2/√2)×(1/2√2)
= 1/2
Hence (sin+ cos)/( sec+ cosecθ ) = 1/2

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If tan = 1 then, find the values of (sin+ cos)/( sec+ cosecθ ).

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