Trigonometry (Basic)

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #41

State true or false.
(i) Value of `sin^2 5\theta + cos^2 5\theta` is 5.
(ii) The maximum value of `sin 3\theta` is 3.
(iii) If `0^\circ \lt \theta \lt \90^\circ`, then, `sin \theta + cos \theta \gt 1`.
(iv) If `0^\circ \lt \theta \le \90^\circ`, then maximum value of `5 + sin \theta` is 7.
(v) If `sin (A+B) = cos (A-B) = 1`, then `A=B=\pi/4`.
(vi) For any angle `\theta`, value of `cos \theta` may be `3/5`
(vii) If `\theta` is a positive acute angle, then value of `tan \theta` is always greater than 1.
(viii) Value of `(sin 12^\circ - cos 78^\circ)` is 1.
Ans: (i) False, (ii) False, (iii) True, (iv) False, (v) True, (vi) True, (vii) False, (viii) False
SEE SOLUTION

Question No: #42

If `sin A + sin B = 2` where `(0^circ \le A,B \le 90^\circ)`, then find the value of `cos A + cos B`.
Ans: `0`
SEE SOLUTION

Question No: #43

If `cos A + cos B = 2` (where, `0^\circ \lt A,B \le 90^\circ`), then value of `sin A + sin B` is -
(a) `0`, (b) `1`, (c) `2`, (d) `\sqrt{2}`
Ans: (a) `0`
SEE SOLUTION

Question No: #44

If `x\ sin 60^\circ cos^2 30^\circ = \frac{tan^2 45^\circ sec 60^\circ}{\text{cosec}\ 60^\circ}`, then find the value of `x`.
Ans: `2 2/3`
SEE SOLUTION

Question No: #45

If `x^2 = sin^2 30^\circ + 4 cot^2 45^\circ - sec^2 60^\circ`, then find the value of `x`
Ans: `\pm 1/2`
SEE SOLUTION

Question No: #46

If `x\ tan 30^\circ + y\ cot 60^\circ = 0` and `2x - y\ tan 45^\circ = 1`, then find the values of `x` and `y`.
Ans: `x = 1/3, y = - 1/3`
SEE SOLUTION

Question No: #47

Calculate the value of following.
(i) `sec^2 60^\circ - cot^2 30^\circ - \frac{2 tan 30^\circ \text{cosec}\quad60^\circ}{1 + tan^2 30^\circ}`.
(ii) `\frac{tan 60^\circ - tan 30^\circ}{1 + tan60^\circ tan 30^\circ} + cos 60^\circ cos 30^\circ + sin 60^\circ sin 30^\circ`.
(iii) `cot^2 30^\circ - 2 cos^2 60^\circ - 3/4 sec^2 45^\circ - 4 sin^2 30^\circ`.
(iv) `\frac{5 cos^2 \frac{\pi}{3} + 4 sec^2 \frac{\pi}{6} - tan^2 \frac{\pi}{4}}{sin^2 \frac{\pi}{6} + cos^2 \frac{\pi}{6}}`.
Ans: (i) `0`, (ii) `\frac{5\sqrt{3}}{6}`, (iii) `0`, (iv) `67/12`
SEE SOLUTION

Question No: #48

Prove that, `\frac{1 - tan^2 30^\circ}{1 + tan^2 30^\circ} = cos 60^\circ`.

Question No: #49

Value of `sin 0^\circ \times sin 1^\circ \times sin 2^\circ \times ... \times sin 90^\circ` is ...........
Ans: `0`
SEE SOLUTION

Question No: #50

Value of `cos 0^\circ \times cos 1^\circ \times cos 2^\circ \times ... \times cos 90^\circ` is ...........
Ans: `0`
SEE SOLUTION