Match List – I with List – II.

Choose the correct answer from the options given below:

A-II, B-IV, C-I, D-III

The correct answer is Option (1) → A-II, B-IV, C-I, D-III

(A) $4 \sin ^{-1} x+\cos ^{-1} x=\pi$

$⇒4\sin ^{-1} x+\left(\frac{π}{2}-\sin ^{-1} x\right)=\pi$

$⇒3\sin ^{-1} x=\frac{π}{2}$

$⇒\sin ^{-1} x=\frac{π}{6}$

$⇒x=\sin\left(\frac{π}{6}\right)=\frac{1}{2}$ (II)

(B) $\frac{1-\tan ^2 15°}{1+\tan ^2 15°}=\tan(45°-15°)=\tan 30°$

$⇒\tan 30°=\frac{\sqrt{3}}{2}$ (IV)

(C) $x+\frac{1}{x}=2$

$⇒x^2-2x+1=0$

$⇒(x-1)^2=0$

$⇒x=1$

$∴\sin^{-1}(1)=\frac{\pi}{2}$ (I)

(D) $θ_3=\pi-(θ_1+θ_2)$

$=\pi-(\cot^{-1}2+\cot^{-1}3)$

$=\pi-\left(\tan^{-1}\frac{1}{2}+\tan^{-1}\frac{1}{3}\right)=\pi=\tan^{-1}\left(\frac{\frac{1}{2}+\frac{1}{3}}{1-\frac{1}{2}×\frac{1}{3}}\right)$

$=\pi-\tan^{-1}1=\pi-\frac{\pi}{4}=\frac{3\pi}{4}$ (III)