If the value of the expression tan⁡1/2cos^(-1)⁡2/(√5) is in the form of a+√b where a, b∈Z, then the value of (a+b)/b is

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MARKS Content Team · Accepted Answer

Correct answer: 0.6. We know that, tan⁡x/2=(1-cos⁡x)/(sin⁡x ) ∴ tan⁡1/2cos^(-1)⁡2/(√5) =(1-cos⁡cos^(-1)⁡2)/(√5)sin⁡cos^(-1)⁡2/(√5) =(1-2/√5)/(sin⁡sin^(-1)⁡1/√5) =(1-2/√5)/(1/√5)=√5-2 Now, a+√b =−2+√5 ⇒a=−2 and b=5 Hence, (a+b)/b =3/5 =0.6

If the value of the expression $\tan (\frac{1}{2} \cos^{- 1} \frac{2}{\sqrt{5}})$ is in the form of $a + \sqrt{b}$ where $a, b \in Z,$ then the value of $\frac{a + b}{b}$ is

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More Inverse Trigonometric Functions Questions

If the value of the expression tan⁡12cos-1⁡25 is in the form of a+ b where a, b∈Z, then the value of a+b b is

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More Inverse Trigonometric Functions Questions

If the value of the expression $\tan (\frac{1}{2} \cos^{- 1} \frac{2}{\sqrt{5}})$ is in the form of $a + \sqrt{b}$ where $a, b \in Z,$ then the value of $\frac{a + b}{b}$ is