>> Elementary Mathematics >> Trigonometry
1). If \( \Large \triangle ABC \) is right angled at C, then what is cos (A + B) + Sin (A + B) equal to?
A). 0 B). \( \Large \frac{1}{2} \)
C). 1 D). 2
2). If \( \Large \alpha \), \( \Large \beta \) and \( \Large \gamma \) are acute angled such that \( \Large sin \ \alpha=\frac{\sqrt{3}}{2} \ cos \ \beta=\frac{\sqrt{3}}{2} \) and tan r=1 then what is \( \Large \alpha + \beta + \gamma \) equal to?
A). 105 degree B). 120 degree
C). 135 degree D). 150 degree
3). If \( \Large tan \ \theta \) = 3/4 and \( \Large \theta \) is acute, then what is the value of \( \Large sin \ \theta \)?
A). \( \Large -\frac{3}{5} \) B). \( \Large \frac{3}{5} \)
C). \( \Large \frac{4}{5} \) D). \( \Large -\frac{4}{5} \)
4). If \( \Large sin \ \theta =\frac{a^{2}-1}{a^{2}+1} \) then the value of \( \Large sec \ \theta + tan \ \theta \) will be
A). \( \Large \frac{a}{\sqrt{2}} \) B). \( \Large \frac{a}{a^{2}+1} \)
C). \( \Large \sqrt{2}a \) D). a
5). If \( \Large \alpha + \beta \)=90 degree and \( \Large \alpha : \beta \)=2:1 then the value of \( \Large sin \alpha : sin \beta \) is
A). \( \Large \sqrt{3}:1 \) B). 2 : 1
C). 1 : 1 D). \( \Large \sqrt{2}:1 \)
6). If \( \Large sin \ \theta + cos \ \theta =1 \), what is the value of \( \Large sin \ \theta \ cos \ \theta \)?
A). 2 B). 0
C). 1 D). 1/2
7). If \( \Large tan \theta \) = 3/4 and \( \Large \theta \) is acute, then \( \Large cosec \theta \) is equal to
A). \( \Large \frac{5}{3} \) B). \( \Large \frac{5}{4} \)
C). \( \Large \frac{4}{3} \) D). \( \Large \frac{3}{4} \)
8). The value of \( \Large \left(\frac{1}{(1+tan^{2} \theta )}+\frac{1}{(1+cot^{2} \theta )}\right) \) is
A). 1 B). 2
C). \( \Large \frac{1}{2} \) D). \( \Large \frac{1}{4} \)
9). The minimum value of \( \Large sin^{2} \theta+cos^{4} \theta \) is
A). \( \Large \frac{1}{\sqrt{2}} \) B). \( \Large \frac{3}{5} \)
C). \( \Large \frac{3}{4} \) D). \( \Large \frac{2}{3} \)
10). If \( \Large sec \theta +tan \theta =2 \), what is the value of \( \Large sec \theta \) ?
A). \( \Large \frac{3}{2} \) B). \( \Large \sqrt{2} \)
C). \( \Large \frac{5}{2} \) D). \( \Large \frac{5}{4} \)