If sin-1-2 and tan-1-3- then the value of - is

The correct option is C π/4Given that, tan θ= 1/2 and tan ϕ= 1/3 Now, tan(θ+ ϕ) = tan θ+tan ϕ/1 tan θ . tan ϕ ⇒ tan(θ+ ϕ)= 1/2+1/3/2 1/2.1/3 ⇒ tan(θ+ ϕ)= 3+2 ...

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Byju's Answer

Standard XII

Mathematics

Trigonometric Ratios for Sum of Two Angles

If sinθ=1/2 a...

Question

If $s i n θ = \frac{1}{2}$ and $t a n ϕ = \frac{1}{3}$ , then the value of $θ + ϕ$ is

\frac{π}{6}

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π

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\frac{π}{4}

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Solution

The correct option is D $\frac{π}{4}$
Given that,
$t a n θ = \frac{1}{2}$ and tan \phi= \frac{1}{3} \)
Now, $t a n (θ + ϕ) = \frac{t a n θ + t a n ϕ}{1 - t a n θ . t a n ϕ}$
$\Rightarrow t a n (θ + ϕ) = \frac{\frac{1}{2} + \frac{1}{3}}{2 - \frac{1}{2} . \frac{1}{3}}$
$\Rightarrow t a n (θ + ϕ) = \frac{\frac{3 + 2}{6}}{\frac{6 - 1}{6}} = \frac{5}{5} = 1$
$\Rightarrow t a n (θ + ϕ) = t a n \frac{π}{4}$
$∴ θ + ϕ = \frac{π}{4}$

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