Question

please answer it ..... i want​

Answer 1

Answer:

cosec²(90-∅)-tan²∅=1

4(cos²48+cos²42)=1

so it is 1/4

then 2tan²30sec²52sin²38=2tan²301/cos²52.cos²52=2tan²30=2/3

then cosec²70-tan²20=1

so this is 1/4-2/3=-5/12

Answer 2

Solution

Let's break the question

→ [cosec²(90° - ∅) - tan²∅]/4(cos² 48° cos² 42°)

Now let's break more into numerator and denominator.

→ cosec²(90° - ∅) - tan²∅

We know cosec(90° - ∅) = sec∅

→ sec²∅ - tan²∅ = 1 [Identity]

Solving denominator

→ 4(cos² 48° + cos² 42°)

→ 4[cos²48° + sin²(90° - 42²)]

→ 4(cos²48° + sin²48°)

→ 4(1) = 4

Fraction: ¼

Solving another part of question

→ (2tan²30° sec²52° sin²38°)/(cosec²70 - tan²20°)

→ [2 × (1/√3)² sec²52° cos²(90° - 38°)]/[sec²(90° - 70°) - tan²20°)

→ [2 × ⅓ sec² 52° cos 52°]/[sec²20° - tan²20°]

Fraction → ⅔

Total Answer = ¼ - ⅔

→ (3 - 8)/12 = - 5/12 [Answer]