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The value of "tan22^(@)30^(')...

The value of `"tan22^(@)30^(')`

A

`(1)/(2 sqrt(2))`

B

`(sqrt(2))/(1+sqrt(2))`

C

`(1)/(sqrt(2)+1)`

D

`(1)/(sqrt(2) -1)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `" "theta=45^(@)`
We know that, `" "tan""(theta)/(2)=(sin""(theta)/(2))/(cos""(theta)/(2))=(2sin""(theta)/(2)*cos""(theta)/(2))/(2cos^(2)""(theta)/(2)) rArrtan""(theta)/(2)=(sintheta)/(1 +costheta)`
`therefore" "tan22^(@)30^(')=(sin45^(@))/(1+cos45^(@))" "[becausetheta=45^(@)]`
` " "=((1)/(sqrt(2)))/(1+(1)/(sqrt(2)))=(1)/(sqrt(2)+1)`
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