Download App

Introduction of Trigonometry — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsIntroduction of Trigonometry2 Marks
Question
Prove the given identity, where the angles involved are acute angles for which the expressions are defined. $\frac { \cos A } { 1 + \sin A } + \frac { 1 + \sin A } { \cos A } = 2 \sec A$
✓

Answer

$L H S = \frac { \cos A } { 1 + \sin A } + \frac { 1 + \sin A } { \cos A }$
$= \frac { \cos ^ { 2 } A + ( 1 + \sin A ) ^ { 2 } } { ( 1 + \sin A ) \cos A } = \frac { \cos ^ { 2 } A + 1 + \sin ^ { 2 } A + 2 \sin A } { ( 1 + \sin A ) \cos A }$
$= \frac { 1 + 1 + 2 \sin A } { ( 1 + \sin A ) \cos A } \because \sin ^ { 2 } A + \cos ^ { 2 } A = 1$
$= \frac { 2 + 2 \sin A } { ( 1 + \sin A ) \cos A } = \frac { 2 ( 1 + \sin A ) } { ( 1 + \sin A ) \cos A }$
$= \frac { 2 } { \cos A } = 2 \cdot \frac { 1 } { \cos A } = 2 \sec A = R H S$

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 Introduction of Trigonometry→Introduction of Trigonometry — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

The minute hand of a clock is 10 cm long. Find the area of the face of the clock described by the minute hand between 9 A.M. and 9.35 A.M.
→
Two concentric circles are of radii $7 \ cm$ and $r \ cm$ respectively, where $r>7$. A chord of the larger circle of length $48 \ cm,$ touches the smaller circle. Find the value of $r$.
→
Write the discriminant of the following quadratic equation.
$x^2 - x + 1 = 0$
→
Is the sequence $0.2, 0.22, 0.222, 0.2222, …$. forms an $AP$? If it forms an $AP$, find the common difference d and write three more terms.
→
In $\triangle\text{ABC},$ ray AD bisects $\angle\text{A}$ and intersects BC in D. If BC = a, AC = b and AB = c, prove that
$\text{BD}=\frac{\text{ac}}{\text{b}+\text{c}}$
→
Find the $10^{\text {th }}$ term from the end of the A.P. $8,10,12, \ldots, 126$.
→
Find the area of the largest triangle that can be inscribed in a semi-circle of radius r units.
→
Find the mode of the following distribution.
Class-interval
10-15
15-20
02-25
25-30
30-35
35-40
Frequency
30
45
75
35
25
15
→
Prove that the points $(3,0),(6,4)$ and $(-1,3)$ are the vertices of an isosceles triangle.
→
Prove that $\frac{\big(\sin^273^\circ+\sin^217\big)}{\big(\cos^228^\circ+\cos^262^\circ\big)}=1.$
→