Math Olympiad Test: Trigonometry- 1 - Free MCQ with solutions Class 10

Given A and B are complementary angles then ∠A + ∠B = 90 (i)
and in ∆ABC ∠A + ∠B + ∠C = 180 (ii)
From (i) and (ii) ∠C = 90
∴ tan ∠C = tan 90 = ∞

Given
sin²20 + sin²70 = sin²20 + [cos(90 - 20)]²
= sin²20 + cos²20 = 1

1 revolution = 2*π radian
Given that
The number of revolutions in 1 hour = 20
So,
The number of revolution in 25 minutes = 20 x 25/60 = 25/3
The radians it run through in 25 minutes = (25/3)2 * π
⇒ 50π^c/3

sec α + tan α = m then sec⁴α - tan⁴α - 2sec α tanα
= (sec²α - tan²α) (sec²α + tan²α) - 2sec α tan α = sec²a + tan²a - 2sec α tan α
= (sec α + tan α) = m²

Given tan (A - 30°) = 2 - √3

Given (cosec A − sinA)(sec A − cosA)(tan A + cotA)

Simplify the numerator and denominator by taking common terms appropriately.

Given:
tan(α+β) = 12 and tan α = 13
We use the formula:

Substitute the values:

12(1 − 13tanβ) = 13 + tanβ
12 − 156tanβ = 13 + tanβ
−156tanβ − tanβ = 13 − 12
−157tanβ = 1
tanβ = −1/157
Correct Option: B