Considering the principal values of inverse trigonometric functions, the value of the expression tan ( 2 sin - 1 ( 2 13 ) - 2 cos - 1 ( 3 10 ) ) is equal to [2026]

Question

Considering the principal values of inverse trigonometric functions, the value of the expression $\tan (2 \sin^{- 1} (\frac{2}{\sqrt{13}}) - 2 \cos^{- 1} (\frac{3}{\sqrt{10}}))$ is equal to: [2026]

Smart Achievers · Accepted Answer

(1)

$Let \sin^{- 1} (\frac{2}{\sqrt{13}}) = θ & \cos^{- 1} (\frac{3}{\sqrt{10}}) = ϕ$

$\sin θ = \frac{2}{\sqrt{13}} & \cos ϕ = \frac{3}{\sqrt{10}}$

$\tan (2 θ - 2 ϕ) = \frac{\tan 2 θ - \tan 2 ϕ}{1 + \tan 2 θ \tan 2 ϕ}$

$(∵ \tan 2 θ = \frac{2 \tan θ}{1 - \tan^{2} θ})$

$= \frac{\frac{12}{5} - \frac{3}{4}}{1 + \frac{12}{5} \cdot \frac{3}{4}}$

$= \frac{33}{56}$

Solution

Q.
Considering the principal values of inverse trigonometric functions, the value of the expression $\tan (2 \sin^{- 1} (\frac{2}{\sqrt{13}}) - 2 \cos^{- 1} (\frac{3}{\sqrt{10}}))$ is equal to: [2026]

1 $\frac{33}{56}$

2 $\frac{16}{63}$

3 $- \frac{33}{56}$

4 $- \frac{16}{63}$

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Solution

Q. Considering the principal values of inverse trigonometric functions, the value of the expression tan(2sin-1(213)-2cos-1(310)) is equal to: [2026]

1 3356

2 1663

3 -3356

4 -1663