Prove that (cosec A- )^2= (1- ) (1+ ) . - Vidyadip

Question

Prove that $(\text{cosec A}-\cot\text{A})^2=\frac{(1-\cos\text{A})}{(1+\cos\text{A})}.$

✓

Answer

$(\text{cosec }\text{A}-\cot\text{A})^2=\frac{(1-\cos\text{A})}{(1+\cos\text{A})}$$\text{LHS}=(\text{cosec }\text{A}-\cot\text{A})^2$
$=\Big(\frac{1}{\sin\text{A}}-\frac{\cos\text{A}}{\sin\text{A}}\Big)^2$
$=\Big(\frac{1-\cos\text{A}}{\sin\text{A}}\Big)^2$
$=\frac{(1-\cos\text{A})^2}{\sin^2\text{A}}$
$=\frac{(1-\cos\text{A})^2}{1-\cos^2\text{A}} $ $\Big[\because\sin^2\theta+\cos^2\theta=1\Big]$
$=\frac{(1-\cos\text{A})(1-\cos\text{A})}{(1-\cos\text{A})(1+\cos\text{A})}$
$=\frac{(1-\cos\text{A})}{(1+\cos\text{A})}=\text{RHS}$
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 Marks Questions" from Trigonometric Identities→Trigonometric Identities — all question types→Maths STD 10 question papers→Maharashtra Board STD 10 question papers→Maharashtra Board question paper generator→

Similar questions

Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.

$2 x^2-7 x+6=0$ check whether$x=-2$ are solutions of the equations.

A card is drawn from a well shuffled pack of 52 playing cards. Find the probability of each event. The card drawn is (i) a red card (ii) a face card

What is the smallest number that, when divided by 35, 56 and 91 leaves remainders of 7 in each case?

Solve the following quadratic equation:$4 - 11x = 3x^2$

A bag contains 5 red, 8 green and 7 white balls, One ball is drawn at random from the bag. What is the probability of getting a white ball or a green ball?

A lot of 20 bulbs contain 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?

The minute hand of a clock is 7.5cm long. find the area of the face of the clock described by the minute hand in 56 minutes.

Evaluate the following:
$\tan48^\circ\tan23^\circ\tan42^\circ\tan67^\circ$

Write the median class of the following distribution:

Classes	0-10	10-20	20-30	30-40	40-50	50-60	60-70
Frequency	4	4	8	10	12	8	4