Question
If sin x + sin 2x = 1 and cos x + cos 2x = 0, find
x.Solution
Given sin x + sin 2x = 1 and cos x + cos 2x = 0. Using the double-angle identities: sin 2x = 2 sin x cos x and cos 2x = 2 cos² x - 1. Substitute sin 2x and cos 2x into the equations: From sin x + 2 sin x cos x = 1, sin x(1 + 2 cos x) = 1. (Equation 1) From cos x + (2 cos² x - 1) = 0, 2 cos² x + cos x - 1 = 0. Solving this quadratic equation gives cos x = 1/2 or cos x = -1. For cos x = 1/2, substitute into Equation 1: sin x(1 + 2 × 1/2) = 1, sin x(1 + 1) = 1, 2 sin x = 1, so sin x = 1/2. Thus, x = 30°. Answer: a) 30°.
Select the option that best expresses the meaning of the bold phrase/group of words.
Several houses had to be demolished to decongest the road. ...
Give one word substitutes for the following from the choices given below them.
 A doctrine that equates God with the forces and laws of universe.
Select the option that can be used as a one-word substitute for the given group of words.
The study of earthquakes
Select the option that can be used as a one-word substitute for the given group of words.
A person who held a job or office before the current holder
She leans back onto the couch, giggling as I swing a makeshift pendulum before her eyes and lower my voice .
...In the following question , a sentence is given followed by five alternatives containing a single word. Among the five alternatives you have to find th...
Impeccable
Select the most appropriate option to substitute the underlined segment in the given sentence. If there is no need to substitute it, select ‘No subst...
Select the most appropriate option that can substitute the bold segment in the given sentence.
Oscar is the most prestigious award which is int...
- Select the most appropriate 'one word' for the expression given below.
A person who studies and writes about the past
...
