Question
Without using tables evaluate:
$\frac{2 \tan 53^{\circ}}{\cot 37^{\circ}}-\frac{\cot 80^{\circ}}{\tan 10^{\circ}}$.
$\frac{2 \tan 53^{\circ}}{\cot 37^{\circ}}-\frac{\cot 80^{\circ}}{\tan 10^{\circ}}$.
✓
Answer
$\frac{2 \tan 53^{\circ}}{\cot 37^{\circ}}-\frac{\cot 80^{\circ}}{\tan 10^{\circ}}$
$ =\left(\frac{2 \tan 53^{\circ}}{\cot \left(90^{\circ}-53^{\circ}\right)}-\left(\frac{\cot 80^{\circ}}{\tan \left(90-80^{\circ}\right)}\right)\right. $
$ =\left(\frac{2 \tan 53^{\circ}}{\tan 53^{\circ}}\right)-\left(\frac{\cot 80^{\circ}}{\cot 80^{\circ}}\right)$
$= 2 - 1$
$= 1$
$ =\left(\frac{2 \tan 53^{\circ}}{\cot \left(90^{\circ}-53^{\circ}\right)}-\left(\frac{\cot 80^{\circ}}{\tan \left(90-80^{\circ}\right)}\right)\right. $
$ =\left(\frac{2 \tan 53^{\circ}}{\tan 53^{\circ}}\right)-\left(\frac{\cot 80^{\circ}}{\cot 80^{\circ}}\right)$
$= 2 - 1$
$= 1$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
In the figure, PA and PB is a pair of tangents drawn to a circle having its centre at O . If $\angle \mathrm{APB}=52^{\circ}$, find $\angle \mathrm{PAB}$ and $\angle \mathrm{PBA}$.
→$
\text { If } a \sin ^2 \theta+b \cos ^2 \theta=c \text { and } p \sin ^2 \theta+q \cos ^2 \theta=r \text {, prove that }(b-c)(r-p)=(c-a)(q-r)
$
→\text { If } a \sin ^2 \theta+b \cos ^2 \theta=c \text { and } p \sin ^2 \theta+q \cos ^2 \theta=r \text {, prove that }(b-c)(r-p)=(c-a)(q-r)
$
Distribution of height in cm of 100 people is given below:
Draw a histogram to represent the above data.
| Class interval (cm) | Frequency |
| 145 - 155 | 3 |
| 155 - 165 | 35 |
| 165 - 175 | 25 |
| 175 - 185 | 15 |
| 185 - 195 | 20 |
| 195 - 205 | 2 |
What should be minimum monthly deposit in a recurring deposit for 3 years to get Rs 20,220 on maturity after 3 years at an interest rate of 8% pa.
In the given figure, AB is the diameter of the circle with centre O.
If ∠ADC = 32°, find angle BOC
If ∠ADC = 32°, find angle BOC
Solve the equation $2 x^2+\sqrt{5} x-5=0$ using formula, write your answer correct to 2 decimal places.
→A shopkeeper buys an article whose list price is ₹ 800 at some rate of discount from a wholesaler. He sells the article to a consumer at the list price and charges sales tax at the prescribed rate of 7.5%. If the shopkeeper has to pay a VAT of ₹ 6, find the rate of discount at which he bought the article from the wholesaler.
Salman buys 50 shares of face value Rs 100 available at Rs 132.
(i) What is his investment?
(ii) If the dividend is 7.5% p.a., what will be his annual income?
(iii) If he wants to increase his annual income by Rs 150, how many extra shares should he
(i) What is his investment?
(ii) If the dividend is 7.5% p.a., what will be his annual income?
(iii) If he wants to increase his annual income by Rs 150, how many extra shares should he
Using the properties of proportion, solve the following equation for $x$; given $\frac{x^3+3 x}{3 x^2+1}=\frac{341}{91}$
→The lengths of the parallel sides of a trapezium are $(x + 9)$ cm and $(2x – 3)$ cm and the distance between them is $(x + 4)$ cm. If its area is $540 cm^2$, find $x$.
→