- A0
- B
- C1
- D5
Step-by-Step Solution
Pair the angles that add to 90°: tan 85° = tan(90° − 5°) = cot 5°, so tan 5° · tan 85° = 1. Likewise tan 25° · tan 65° = 1. With tan 45° = 1, the whole product is 1 · 1 · 1 = 1.
Answer: C) 1
Find the value of tan 5° · tan 25° · tan 45° · tan 65° · tan 85°.
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.
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