- A
- B
- C2
- D
Step-by-Step Solution
sec θ = 2 means cos θ = , so θ = 60° and tan θ = . Check with the identity taθ = seθ − 1 = 4 − 1 = 3.
Answer: A)
If sec θ = 2 for an acute angle θ, find tan θ.
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
If sin θ = 2/3 for an acute angle θ, find cos θ.If sin θ = 12/37 for an acute angle θ, find the value of cos θ − sin θ.If tan θ = 3/4 for an acute angle θ, find the value of 1 - θ/1 + θ.If cosec θ = √5 for an acute angle θ, find cot θ.For an acute angle θ, which one of these values is POSSIBLE for sec θ?