Question

If tan theta =4/3, find the value of sin theta+cos theta/sin theta-cos theta.

Answer 1

tan theta=4/3
tan theta=p/b
p=4,and b=3

by paithagoras theorem,
H=root under P^2+B^2
H=root under 4^2+3^2
H=root under 16+9
H=root under 25
H=5

sin theta=p/h
sin theta=4/5
cos theta=b/h
cos theta=3/5

sin theta+cos theta/sin theta-cos theta
=4/5+3/5 by 4/5-3/5
=4+3/5by4-3/5
=7/5by1/5
=7/5×5/1
=7/1
=7

hope it will help you.

Answer 2

Concept: In right angled triangle, Sinθ=P/H, Cosθ=B/H, Tanθ=P/B.

A theorem attributed to pythagoras that the sq. on the flank of a 90° triangle is equal in space to the add of the squares on the opposite 2 sides.

According to the pythagoras theorem,

$H^{2}= B^{2}+ P^{2}$

Trigonometry could be a branch of arithmetic that studies relationships between facet lengths and angles of triangles.

Full form of Tanθ=Tangent

Cosθ= Cosine

Sinθ= Sine

Given: Tanθ=4/3

Find: Sinθ+Cosθ/Sinθ-Cosθ Find the value of this equation.

Solution:

Tanθ=4/3=P/B

By using pythagoras theorem,

$H^{2}= B^{2}+ P^{2}$

H^2= 9+16

H=5

Sinθ=P/H

      =4/5

Cosθ=B/H

       =3/5

Sinθ+Cosθ/Sinθ-Cosθ

4/5+3/5 / 4/5-3/5

7/5 / 1/5

=7

Final answer: 7

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