If \(\sin 44^{\circ}=x\), then the value of \(\tan 46^{\circ}\) will be:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\frac{\sqrt{1-x^2}}{x}\)
44° and 46° are complementary angles (they add up to 90°), so \(\tan 46^{\circ}=\tan(90^{\circ}-44^{\circ})=\cot 44^{\circ}\). Cot 44° is then written with sin 44° \(=x\).
\(\cos 44^{\circ}=\sqrt{1-\sin^{2}44^{\circ}}=\sqrt{1-x^{2}}\) (cos 44° is positive, as 44° is acute)
\(\displaystyle \tan 46^{\circ}=\cot 44^{\circ}=\frac{\cos 44^{\circ}}{\sin 44^{\circ}}=\frac{\sqrt{1-x^{2}}}{x}\)