2018 Question Paper Solution | Question 5

This 1-mark question is from the chapter Trigonometry. Concept tested: Trigonometric values of complementary angles.

Question 5: What is the value of (cos² 67° - sin² 23°)?

Video Explanation

Explanatory Answer | Q5 2018 Board Paper

The given trigonometric expression is cos²67° – sin²23°
The expression is of the form (a² - b²)
(a² - b²) = (a + b)(a - b)
∴ cos²67° – sin²23° = (cos 67° + sin 23°) (cos 67° - sin 23°) ... eqn(1)

Trigonometric Ratio of Complementary Angles: sin (90 - θ) = cos θ
Let us express sin 23° = sin(90° - 67°)
sin (90° - 67°) = cos 67°

Substitute sin 23° as cos 67° in eqn(1)
(cos 67° + sin 23°) (cos 67° - sin 23°) = (cos 67° + cos 67°) (cos 67° - cos 67°)
(2 cos 67°) (0) = 0.