correct answer will be brainlist
pls solve it
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correct answer will be brainlist
pls solve it
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GIVEN:
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!
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INFO(Trigonometry):-
→ sin²A + cos²A = 1
→ sec²A - tan²A = 1
→ cosec²A - cot²A = 1