Question

correct answer will be brainlist
pls solve it​

Answer 1

GIVEN:

• In ∆ABC angle C = ,90°
• In ∆ABC ↓

Hypotenuse = AC

Base = BC

Height = AB

TO PROVE:

cosec²A - tan²B = 1

Using , Angle sum property

♦ Angle sum property : Sum of all angles in a triangle = 180°

angle C = 90°

Angle A + angle B + angle C = 180°

Angle A + angle B = 180° - 90°

Angle B = 90° - angle A

____________________________

____________________________

→ cosec²A - tan²B = 1

Taking LHS

→ cosec²A - tan²B

Substituting angle B = 90° - A

→ cosec²A - tan²(90° - A)

We know that

★ tan(90° - A) = cotA

→ cosec²A - cot²A

Using Identity

cosec²θ - cot²θ = 1

Similarly

→ cosec²A - cot²A = 1

LHS = RHS

Hence proved!

MORE

INFO(Trigonometry):-

→ sin²A + cos²A = 1

→ sec²A - tan²A = 1

→ cosec²A - cot²A = 1