Prove that the following identities: Sec A( 1 + sin A)( sec A - t… - Vidyadip

Question

Prove that the following identities:
Sec A( 1 + sin A)( sec A - tan A) = 1.

✓

Answer

LHS = sec A(1 + sin A )( sec A - tan A)
$=\frac{1}{\cos A}(1+\sin A)\left(\frac{1}{\cos A}-\frac{\sin A}{\cos A}\right)$
$=\frac{1}{\cos A}(1+\sin A)\left(\frac{1-\sin A}{\cos A}\right)$
$=\frac{1-\sin ^2 A}{\cos ^2 A}=\frac{\cos ^2 A}{\cos ^2 A}$
= 1
= RHS
Hence proved.

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 Mark Question Answer]" from Trigonometry→Trigonometry — all question types→Mathematics STD 10 question papers→ICSE Board STD 10 question papers→ICSE Board question paper generator→

Similar questions

Prove.$\frac{1+\sin A}{1-\sin A}=\frac{c o \sec A+1}{c o \sin A-1}$

If $sinA + cosA = p$ and $secA + cosecA = q,$ then prove that: $q(p^2 - 1) = 2p$

From 25 identical cards, numbered 1, 2, 3, 4, 5, ……, 24, 25: one card is drawn at random. Find the probability that the number on the card drawn is a multiple of : 5

A watch is listed at Rs 15,500 and the sales tax on it is 18%. Find the selling price of the watch.

If $A =\left|\begin{array}{l}1215 \\ 1117\end{array}\right|$ and $B =\left|\begin{array}{ll}2 & 7 \\ 4 & 9\end{array}\right|$ find $A -2 B$

Find the sub-duplicate ratio of $\frac{1}{4}: \frac{1}{9}$

Find without division, the remainder in the following:
$5x^2 - 9x + 4$ is divided by $(x - 2)$

The surface area of a solid metallic sphere is $2464 cm^2.$ It is melted and recast into solid right circular cones of radius $3.5 cm$ and height $7 cm.$ Calculate: the radius of the sphere $($Take $\pi = 22/7)$

A die is thrown once. Find the probability of getting : an even number

For triangle $\text{ABC},$ show that : $\frac{\sin (A+B)}{2}=\frac{\cos C}{2}$