- A1
- B1681/81
- C1681/1600
- D1600/1681
Step-by-Step Solution
, so . Check: and , so the identity holds.
Answer: C) 1681/1600
Using right triangle PQR (∠°), find the value of 1 + taθ for the angle θ marked at P.
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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