Prove the given identity, where the angles involved are acute ang… - Vidyadip

Question

Prove the given identity, where the angles involved are acute angles for which the expressions are defined. (cosec A - sin A) (sec A - cos A) = $\frac { 1 } { \tan A + \cot A }$
[Hint: Simplify LHS and RHS separately]

✓

Answer

LHS
$= ( \csc A - \sin A ) ( \sec A - \cos A )$
$= \left( \frac { 1 } { \sin A } - \sin A \right) \left( \frac { 1 } { \cos A } - \cos A \right) = \frac { 1 - \sin ^ { 2 } A } { \sin A } \frac { 1 - \cos ^ { 2 } A } { \cos A }$
$= \frac { \cos ^ { 2 } A } { \sin A } \frac { \sin ^ { 2 } A } { \cos A } , \ldots \ldots \ \because \sin ^ { 2 } A + \cos ^ { 2 } A = 1 = \frac { \frac { \sin A \cos A } { \sin A \cos A } } { \frac { \sin ^ { 2 } A } { \sin A \cos A } + \frac { \cos ^ { 2 } A } { \sin A \cos A } }$
........ Dividing the numerator and denominator by sin A cos A
$= \frac { 1 } { \tan A + \cot A }$
= 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 "1 Marks Question" 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

In a simultaneous throw of pair of dice, find the probability of getting:An even number on one and a multiple of 3 on the other.

Evaluate: $\frac{\tan 65^{\circ}}{\cot 25^{\circ}}$

Write the set of values of 'a' for which the equation $x^2+a x-1=0$ has real roots.

Evaluate the following:
$\big(\sin^230^\circ+4\cot^230-\frac34\sec^260^\circ\big)\big(\text{cosec}^245^\circ\sec^230^\circ\big)$

A black die and a white die are thrown at the same time. Write all the possible outcomes. What is the probability?
That the sum of the numbers appearing on the top of the dice is less than or equal to $12$?

Evaluate the following:
$\cos45^\circ\cos30^\circ+\sin45^\circ\sin30^\circ$

Show that 5 x 11 x 17 + 3 x 11 is a composite number.

The following numbers are irrational?
0.232332333...

Classify the following number as rational or irrational:$\big(3+\sqrt{2}\big)$

In the table given below, the times taken by 120 athletes to run a 100 m hurdle race are given:

Class	13.8-14	14-14.2	14.2-14.4	14.4-14.6	14.6-14.8	14.8-15
Frequency	2	4	15	54	25	20

Find the number of athletes who completed the race in less than 14.6 seconds.