Introduction to Trigonometry

Q. 4/5tan²60 + 3sin²60

Q.

Similar figures are always congruent, whereas the congruent figures are not necessarily similar.

1. True

2. False

Q.

If sinA = cosA, find 2tan²A + sin²A - 1

Q. 5sin30+3tan45

Q.

If sinA=cosA, find the value of :

2 tan square A - 2sec square A +5

Q.

If tan(A+B)=√3 and tan A=1 then find angle B

Q.

Question 1- sin 6 degree * sin 42 degree * sin 66 degree * sin 78 degree = ?

Question 2 - cos 6 degree* cos 42 degree * cos 66 degree * cos 78 degree =?

Q. If sin A = 1 and cos B = 1, then find the value of A+B?

1. 30 degrees
2. 45 degrees
3. 60 degrees
4. 90 degrees

Q.

In the adjoining figure, PQ || BC, the what could be the values of AQ & QC respectively

1. 3 cm and 4 cm

2. 2 cm and 6 cm

3. 3 cm and 6 cm

4. 1 cm and 6 cm

Q.

The value of sin 60^o cos 30^o +cos 60^o sin30^o is

1. 1

2. 2

3. -2

4. 0

Q. If sin x = (21/29) , find the value of tan x.

1. (20/29)
2. (21/20)
3. (20/21)
4. (29/20)

Q. From the figure given below, find the value of sin y.

1. (12/20)
2. (13/20)
3. (16/20)
4. (21/20)

Q. Show that

(i) tan 7$°$, tan 23$°$, tan 60$°$, tan 67$°$, tan 83$°$ = $\sqrt{3}$

Q. If tan $\theta$ + cot $\theta$ = 2, find the value of tan² $\theta$ + cot² $\theta$

Q. Find the value of the following.
(i) $\frac{\sin 50°}{\cos 40°}+\frac{\cos ec40°}{sec50°}-4\cos 50°.\cos ec40°$

Q. If A and B are acute angles and sin A = cos B, show that A + B = 90$°$.

Q. If tan 2A = cot (A $-$18$°$) then find the value of A where (2A) and (A-18$°$) are acute angles.

Q.

The cofunction of sin45 is

1. sin35

2. cos35

3. cos45

4. cos25

Q. $△ABC$ is a right angled triangle. Find the value of the
$cose{c}^{2}A+si{n}^{2}B-co{t}^{2}A$.

1. 0
2. -1
3. 1
4. 2

Q. Verify that tan 30$°$ = $\frac{\tan 60°-\tan 30°}{1+\tan 60°\tan 30°}$

Q. Calculate the value of A
1 . ( sin A -1) (2 cos A -1) = 0
2. ( tan A -1) ( cosec 3A -1 ) = 0

Q. Find the values of the following
(i) 2 tan ^₂ 45$°$ + cos ^₂ 30 $-$ sin ^₂ 60$°$
(ii) 4cot ^₂ 45$°$ $-$ sec ^₂ 60$°$ + cosec ^₂ 30$°$+cot 90$°$

Q.

If sin (2A − 3B) = cos (3A + 8B), where (2A − 3B) and (3A + 8B) are acute angles, then what is the value of (A + B)?

1. 23°

2. 25°

3. 18°

4. 12°

Q. (i) If cos(40$°$ + x) = sin 30$°$ find the value of x.
(ii) If tan y = sin 45$°$ + cos 45$°$ then find the value of y.

Q. Find the values of the following.
(i) cos 38$°$ cos 52$°$ $-$ sin 38$°$ sin 52$°$

(ii) $\frac{\cos 80°}{\sin 10°}+\cos 59°\cos ec31°$

(iii) $\frac{2\tan 53°}{cot37°}-\frac{\cos 80°}{\tan 10°}$

Q. Find the value of x,
If sin2x = sin60$°$ cos 30$°$ $-$ cos 60$°$ sin 30$°$

Q. If A = 60$°$ B = 30$°$ then show that cos(A$-$B) = cosA.cosB + sin A. sin B

Q.

If 3cot A=4, then find cos² A - sin² A

1. 25/7

2. 7/25

3. 1/25

4. 22/7

Q. 2(cos⁴ 60$°$ + sin⁴ 30$°$) $-$ (tan² 60$°$ + cot² 45$°$) + 3sec² 30$°$ = $\frac{1}{4}$

Q. Coz (40-x)° =sin30°