Question
If \(\rm \sin θ+\cos θ=\frac{\sqrt{11}}{3}\), then what is tan θ + cot θ equal to?
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SSC Selection Post 2023 Graduation Level Question Paper (30 Jun, 2023) (Shift 1)
The correct answer is
9
The correct answer is 9.
(\sin \theta + \cos \theta)^2 = \sin^2 \theta + \cos^2 \theta + 2 \sin \theta \cos \theta = 1 + 2 \sin \theta \cos \theta Similarly, when you square the difference: (\sin \theta - \cos \theta)^2 = \sin^2 \theta + \cos^2 \theta - 2 \sin \theta \cos \theta = 1 - 2 \sin \theta \cos \theta These expansions are very useful in solving trigonometric problems where sums or differences of sine and cosine are given, and products or other related functions like tangent and cotangent need to be found.
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Important Questions from Trigonometric Identities
- If $\sec\theta + \tan\theta = s$, then find the value of $\frac{s^2-1}{s^2+1}$.
- Find the value of $\frac{\sin A - 2\sin^3 A}{2\cos^3 A - \cos A} + \sqrt{\text{cosec}^2 A - 1}$.
- Solve the following:
$(\text{cosec}23^{\circ}-\text{sin}23^{\circ}) (\text{tan}23^{\circ} + \text{cot}23^{\circ}) (\text{sec}23^{\circ}-\text{cos}23^{\circ})$ If $M = \sqrt{\frac{1+\cos A}{1-\cos A}} - \text{cosec} A - \cot A$, and A is an acute angle, then value of M is
- If
$x = a \text{ cosec}A \text{ sin} B,$
$y = b \text{ cosec}A \text{ cos} B,$ and
$z = c \text{ cot} A,$
then, what is the value of $\frac{x^2}{a^2} + \frac{y^2}{b^2} - \frac{z^2}{c^2}$?
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