- A1
- B2
- C0
- D4
Step-by-Step Solution
Expanding, the cross terms +2 sin θ cos θ and −2 sin θ cos θ cancel, leaving 2 siθ + 2 coθ = 2(siθ + coθ) = 2 · 1 = 2.
Answer: B) 2
For any angle θ, the expression always equals:
Class 10Introduction to TrigonometryTrigonometry
Key idea: Why ratios — and not lengths
Two right triangles with the same acute angle θ are SIMILAR (Class 10 ch. 6 — AA criterion: both have a right angle and the angle θ).
Similar triangles → corresponding sides in fixed ratio.
So the ratio (opposite / hypotenuse) takes the SAME value in any right triangle with angle θ — regardless of how big the triangle is.
That's why sin θ, cos θ, tan θ are FUNCTIONS of the angle alone — they're well-defined.
This is the fundamental reason trigonometry works as a clean theory.
Similar triangles → corresponding sides in fixed ratio.
So the ratio (opposite / hypotenuse) takes the SAME value in any right triangle with angle θ — regardless of how big the triangle is.
That's why sin θ, cos θ, tan θ are FUNCTIONS of the angle alone — they're well-defined.
This is the fundamental reason trigonometry works as a clean theory.
Master this chapter in 30 minutes a day.
Don't just memorise the answer — build a daily practice habit.
Practice 5 Similar Questions Free →All Introduction to Trigonometry practice questions
More Class 10 Introduction to Trigonometry practice
A student claims that for some angle θ, sin θ = 4/3. Is this possible?Two right triangles of very different sizes each contain the same acute angle θ. How do…As θ increases from 0° towards 90°, the value of tan θ:A staircase has 5 equal steps, each 20 cm high and 21 cm deep. The orange line through…Using right triangle PQR (∠Q = 90°), find the value of 1 + tan²θ for the angle θ marked…