Question Text
Question 1 :
If $\sec 4A = cosec\ \begin{pmatrix}A – 20^{\circ}\end{pmatrix}$, where 4A is an acute angle, find the value of A.
Question 2 :
The value of $\cos \theta$ increases as $\theta$ increases. True or False?
Question 6 :
(1 + tan θ + sec θ) (1 + cot θ – cosec θ) = ____
Question 7 :
Can all the other trigonometric ratios of ∠ A be written in terms of sec A?
Question 8 :
If A, B and C are interior angles of a triangle ABC, then $\sin\begin{pmatrix}\frac{B+C}{2}\end{pmatrix}\ne\cos\begin{pmatrix}\frac{A}{2}\end{pmatrix}$. TRUE or FALSE ?
Question 11 :
The value of $\sin \theta$ increases as $\theta$ increases. True or False?
Question 16 :
Is this equality correct ? $\frac{tan A}{1- cotA} + \frac{cotA}{1-tanA}= 1+ secAcosecA$
Question 20 :
(sec A + tan A) (1 – sin A) = ______
Question 21 :
If $\tan 2A = \cot \begin{pmatrix}A – 18^{\circ}\end{pmatrix}$, where 2A is an acute angle, find the value of A.
Question 22 :
Express $\sin 67^{\circ} + \cos 75^{\circ}$ in terms of trigonometric ratios of angles between $0^{\circ}$ and $45^{\circ}$.
Question 23 :
Is $\frac{cos A – sin A + 1}{cos A + sin A - 1}= cosecA + cotA$?
Question 24 :
$\cos 38^{\circ} \cos 52^{\circ} – \sin 38^{\circ} \sin 52^{\circ} \ne 0$. TRUE or FALSE?
Question 27 :
Is this equality correct ?$(cosec A – sin A) (sec A – cos A)= \frac{1}{tan A +cot A}$
Question 30 :
Can the trigonometric ratios sin A, sec A and tan A be expressed in terms of cot A?