- A18°
- B24°
- C27°
- D36°
Step-by-Step Solution
cot°) = tan(90° − °)) = tan(108° − A). So ° − A, giving ° and °. (Check: tan 72° = cot 18°.)
Answer: D) 36°
If tan = cot°), where is an acute angle, find A.
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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Find the value of tan 5° · tan 25° · tan 45° · tan 65° · tan 85°.For an acute angle θ, simplify √1 - ^2 θ/ ^2 θ.Simplify: (cosec θ − cot θ)(cosec θ + cot θ).For any angle θ, the expression (sin θ + cos θ)² + (sin θ − cos θ)² always equals:A student claims that for some angle θ, sin θ = 4/3. Is this possible?