Question

If `theta` is a positive acute angle and `3(sec^(2)theta+tan^(2)theta)=5`, then the value of `cos 2theta ` is(यदि धनात्मक न्यून कोण है और `3(sec^(2)theta+tan^(2)theta)=5` है तो `cos 2theta ` का मान है )
A. `(1)/(2)`
B. `(sqrt3)/(2)`
C. `(1)/(sqrt2)`
D. 1

Answer 1

Correct Answer - a
`3(sec^(2)theta+tan^(2)theta)=5`
`sec^(2)theta+tan^(2)theta=(5)/(3)` ...(i)
`sec^(2)theta-tan^ (2)theta=1` ......(ii)
Add eqn. (i) `&` (ii)
`2sec^(2)theta=(8)/(3)`
` sec theta=(2)/sqrt(3)`
`therefore theta=30^ (@)`
`cos2theta=cos2(30^(@))=cot60^(@)=(1)/(2)`