Exercise 10.1 Class 12 Math Solutions - Unit 10 Solution of Trigonometric Equations, Punjab Board

Exercise 10.1 opens Unit 10: Solution of Trigonometric Equations in Class 12 Mathematics under the Punjab Board PCTB / PECTAA curriculum. A trigonometric equation is an equation containing trigonometric functions of an unknown variable angle (\theta) that is satisfied only by certain particular values of (\theta). The values of (\theta) lying in the interval ([0, 2\pi)) that satisfy the equation are known as the Principal Solutions.

To solve basic trigonometric equations (such as (\sin\theta = k), (\cos\theta = k), or (\tan\theta = k)), students first calculate the reference angle (\theta_r = \sin^{-1}|k| \in [0, \frac{\pi}{2}]). Using the signs of trigonometric functions across the four coordinate quadrants (the ASTC rule), students determine the two principal angles in ([0, 2\pi)). Because trigonometric functions are periodic, infinitely many solutions exist. Adding integer multiples of the fundamental period ((2n\pi) for sine, cosine, cosecant, and secant; (n\pi) for tangent and cotangent, where (n \in \mathbb{Z})) produces the complete General Solution set. The exercise also covers algebraic techniques such as factoring quadratic trigonometric equations and applying double-angle identities to reduce equations to linear factors.

For Punjab Board HSSC Part 2 examinations across all nine educational divisions (Lahore, Rawalpindi, Gujranwala, Faisalabad, Multan, Bahawalpur, Sargodha, Sahiwal, and D.G. Khan), Exercise 10.1 is a vital source of Section B Short Questions (finding principal and general solutions of linear and quadratic trigonometric equations) and Section C Long Questions. These step-by-step solutions provide clean quadrant evaluations, exact radian angles, and complete set-builder general solution expressions for every textbook problem.