Download App

Trigonometric Functions — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Functions5 Marks
Question
If $\sec(\text{x}+\alpha)+\sec(\text{x}-\alpha)=2\sec\text{x},$ prove that $\cos\text{x}-\pm\sqrt{2}\cos\frac{\alpha}{2}$
✓

Answer

We have,
$\sec(\theta+\alpha)+\sec(\theta-\alpha)=2\sec\theta.$
$\Rightarrow\frac{1}{\cos^2\theta.\cos^2\alpha-\sin^\theta\sin^2\alpha}+\frac{1}{\cos\theta.\cos\alpha-\sin\theta\sin\alpha}=\frac{2}{\cos\theta}$
$\Rightarrow\frac{2\cos\theta\cos\alpha}{\cos^2\cos^2\alpha-\sin^2\sin^2\alpha}=\frac{2}{\cos\theta}$
$\Rightarrow\frac{2\cos\theta\cos\alpha}{\cos^2\theta\cos^2\alpha-(\cos^2\alpha+\sin^2\alpha)}=\frac{1}{\cos\theta}$
$\Rightarrow\cos^2\theta\cos\alpha=\cos^2\theta(\cos^2\alpha+\sin^2\alpha)-\sin^2\alpha$
$\Rightarrow\cos^2\theta(1-\cos\alpha)=\sin^2\alpha$
$\Rightarrow\cos^2\theta=\frac{\sin^2\alpha}{2\sin^2\frac{\alpha}{2}}$
$=\frac{1\sin^2\frac{\alpha}{2}.\cos^2\frac{\alpha}{2}}{2\sin^2\frac{\alpha}{2}}$
$\Rightarrow\cos\theta=\pm\sqrt{2}\cos\frac{\alpha}{2}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Trigonometric Functions→Trigonometric Functions — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

If the term free from x in the expansion of $\sqrt{\text{x}}-\frac{\text{k}}{\text{x}^2}^{10}$ is 405, find the value of k.
→
Find the equation of the straight line passing through the point of intersection of the lines 5x - 6y - 1 = 0 and 3x + 2y + 5 = 0 and perpendicular to the line 3x - 5y + 11 = 0
→
Find the equation of the parabola whose focus is (1, -1) and whose vertex is (2, 1). Also find its axis and latus rectum.
→
A person observes the angle of elevation of the peak of a hill from a station to be $\alpha.$ He walks c metres along a slope inclined at an angle $\beta$ and finds the angle of elevation of the peak of the hill to be $\gamma.$ Show that the height of the peak above the ground is $\frac{\text{c}\sin\alpha\sin(\gamma-\beta)}{(\sin\gamma-\alpha)}.$
→
For any two sets A and B, prove the following:
$\text{A}-\text{(A}-\text{B})=\text{A}\cap\text{B}$
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{5\text{x}+4\sin3\text{x}}{4\sin2\text{x}+7\text{x}}$
→
Find the equation of the hyperbola, referred to its principal axes as axes of coordinates, in the following cases:
Conjugate axis is 7 and passes throught the point (3,-2)
→
Match the questions given under Column C1 with their appropriate answers given under the Column C2: The value of the λ, if the lines (2x + 3y + 4) + λ (6x - y + 12) = 0 are:
Column C1 Column C2
(a) Parallel to y-axis is (i) $\lambda=-\frac{3}{4}$
(b) Perpendicular to 7x + y - 4 = 0 is (ii) $\lambda=-\frac{1}{3}$
(c) Passes through (1, 2) is (iii) $\lambda=-\frac{17}{41}$
(d) Parallel to x axis is (iv) $\lambda=3$
→
Prove that:
$\tan20^\circ\tan40^\circ\tan60^\circ\tan80^\circ=3$
→
If |z + 1| = z + 2(1 + i), then find z.
→