Trigonometry practice

Q1. If $$ \sin A - \sqrt{6}\,\cos A = \sqrt{7}\,\cos A $$ then $$ \cos A + \sqrt{6}\,\sin A =\;? $$
Options: (1) \(\sqrt{6}\sin A\)  (2) \(\sqrt{7}\sin A\)  (3) \(\sqrt{6}\cos A\)  (4) \(\sqrt{7}\cos A\)


Answer: (2) \(\sqrt{7}\sin A\) 

Q2. The minimum value of $$ 7\cos \theta + 24\sin \theta $$ is ?
Options: (1) 25  (2) -7  (3) -25  (4) None

Answer: -25

Q3. Let $$ \sin(2x)=\frac{1}{7}. $$ Find the numerical value of $$ \sin(x)\sin(x)\sin(x)\sin(x)\;+\;\cos(x)\cos(x)\cos(x)\cos(x). $$


Answer: 97/98

Q4. Let x be a real number such that $$ \sec x - \tan x = 2. $$ Then $$ \sec x + \tan x =\;? $$
Options: (A) 0.1  (B) 0.2  (C) 0.3  (D) 0.4  (E) 0.5


Answer: (E) 0.5


Q5. If $$ \sin(x) = 3\cos(x) $$ then what is $$ \sin(x)\cdot\cos(x)\;? $$
Options: (A) \(\tfrac{1}{6}\)  (B) \(\tfrac{1}{5}\)  (C) \(\tfrac{2}{9}\)  (D) \(\tfrac{1}{4}\)  (E) \(\tfrac{3}{10}\)

Answer: (E) 3/10

Q6. In a right triangle the square of the hypotenuse is equal to twice the product of the legs. One of the acute angles of the triangle is:
Options(all in degrees): (A) 15  (B) 30  (C) 45 (D) 60  (E) 75


Answer: (C) 45


Q7. Suppose that $$ \sin a + \sin b = \sqrt{\frac{5}{3}} \quad\text{and}\quad \cos a + \cos b = 1. $$ What is $$ \cos(a - b)\;? $$
Answer: 1/3

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