Download App

Trigonometric Ratios Of Compound Angles — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Ratios Of Compound Angles2 Marks
Question
Prove that:
$\frac{\cos\text{x}}{1-\sin\text{x}}=\tan(\frac{\pi}{4}+\frac{\pi}{2})$
✓

Answer

$\text{LHS}=\frac{\cos\text{x}}{1-\sin\text{x}}$
$\frac{\cos^2\frac{\text{x}}{2}-\sin^2\frac{\text{x}}{2}}{\sin^2\frac{\text{x}}{2}+\cos^2\frac{\text{x}}{2}-2\sin\frac{\text{x}}{2},\frac{\cos\text{x}}{2}}$ $[\because\cos2\text{x}=\cos^2\text{x}-\sin2\text{x}\ \&\sin^2\text{x}+\cos^2\text{x}]=1$
$\frac{(\cos\frac{\text{x}}{2}-\sin\frac{\text{x}}{2})(\cos\frac{\text{x}}{2}+\sin\frac{\text{x}}{2})}{(\cos\frac{\text{x}}{2}-\sin\frac{\text{x}}{2})}$ 
$=\frac{\cos\frac{\text{x}}{2}+\sin\frac{\text{x}}{2}}{\cos\frac{\text{x}}{2}-\sin\frac{\text{x}}{2}}$ 
Dividing numeretor and denominator by $\cos\frac {\text{x}}{2}$
$=\frac{1+\tan\frac{\text{x}}{2}}{1=\tan\frac{\text{x}}{2}}$
$\tan(\frac{\pi}{4}+\frac{\text{x}}{2})=\text{RHS}$

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 "2 Marks Questions" from Trigonometric Ratios Of Compound Angles→Trigonometric Ratios Of Compound Angles — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\text{a}^\text{x}-\text{a}^{\text{-x}}}{\text{x}}$
→
Find the sum of the series: 3 + 5 + 7 + 6 + 9 + 12 + 9 + 13 + 17 + ... to 3n terms.
→
Assume that P(A) = P(B) show that A = B.
→
If a is the G.M. of 2 and $\frac14,$ find a.
→
Reduce the equation x - y = 4 into normal form. Find their perpendicular distance from the origin and angle between perpendicular and the positive X-axis.
→
Is it true that for any sets A and B, $P(A) \cup P(B) = P(A \cup B)?$Justify your answer.
→
Find the distance of the point (3, -5) from the line 3x - 4y - 26 = 0
→
Find the magnitude, in radians and degrees, of the interior angle of a regular.
heptagon.
→
In a $\triangle\text{ABC},$ Prove that:
$\cos(\text{A+B})= \cos (\pi-\text{C})=0$
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow1}\Big(\frac{1}{\text{x}^2+\text{x}-2}-\frac{\text{x}}{\text{x}^3-1}\Big)$
→