What are trigonometric Ratios and their real life applications?

Number of solution of the equation |cos x| = sin x for $x\in \left[-4\pi ,4\pi \right]$ $$ will be equal to 4 times the number of solutions of the same equation for $x\in \left[0,2\pi \right]$ $$

Graphs of y = |cos x| and y = sin x are as shown below.

Hence, two solutions of given equation in [0, 2]

$$ $\Rightarrow$  total of 8 solutions in [4, 4]

sin (A + B) = sinA cosB + cosA sinB

sin (A - B) = sinA cosB - cosA sinB

cos (A + B) = cosA cosB - sinA sinB

cos (A - B) = cosA cosB + sinA sinB

tan (A + B) = (tanA + tanB) / (1 - tanA tanB)

tan (A - B) = (tanA - tanB) / (1 + tanA tanB) 

Double Angle Formulas:

sin 2? = 2 sin? cos?

cos 2? = cos²? - sin²? = 2cos²? - 1 = 1 - 2sin²?

tan 2? = 2 tan? / (1 - tan²? ) 

Triple Angle Formulas:

sin 3? = 3 sin? - 4 sin³?

cos 3? = 4 cos³? - 3 cos?

Questions from below topics can be asked in the Class 12 exams 2026 CBSE-

Positive and negative angles. Measuring angles in radians and in degrees and conversion from
one measure to another. Definition of trigonometric functions with the help of unit circle. Truth of
the identity sin2x + cos2x = 1, for all x. Signs of trigonometric functions. Domain and range of
trigonometric functions and their graphs. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny,
cosx & cosy and their simple applications. Deducing identities etc.

You can download the complete CBSE 12th Mathematics syllabus 2026 by clicking here