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Find the value of theta if sec^(2)theta...

Find the value of `theta` if `sec^(2)theta+tan^(2)theta=(5)/(3)`and`theta` lies in first quadrant.

Text Solution

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`sec^(2)theta+tan^(2)theta=(5)/(3)`
`rArr1+tan^(2)theta+tan^(2)theta=(5)/(3)rArr2tan^(2)theta=(5)/(3)-1=(2)/(3)`
`rArrtan^(2)theta=(1)/(3)rArrtan^(2)theta=((1)/(sqrt(3)))^(2)`
`rArrtantheta=(1)/(sqrt(3))` (taking positive sign only)
`rArrtantheta=tan30^(@)rArrtheta=30^(@)`
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