Math, asked by muttu93mk, 11 months ago

prove that 1+cot2 theta/1+cosec2theta = cosec theta​

Answers

Answered by Anonymous
4

The terminal side of an angle θ in standard position intersects the unit circle at the point (cosθ,sinθ). If

θ≠π2+nπ,n∈Z

draw a segment perpendicular to the terminal side of the angle. Since two angles complementary to the same angle are congruent, the angle formed by the perpendicular to the terminal side of the angle θ in standard position and the y-axis has measure θ. Since the leg opposite angle θ in this triangle has length 1, the hypotenuse has length |cscθ| and the leg adjacent to angle θ has length |cotθ|. By the Pythagorean Theorem,

1+|cotθ|21+cot2θ=|cscθ|2=csc2θ

Answered by Anonymous
0

Answer:

Identity : cosec

2

A−cot

2

A=1

LHS =(1+cot

2

A)sin

2

A

=cosec

2

A×sin

2

A

=

sin

2

A

1

×sin

2

A

=1

=RHS

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