Question

If sec θ = 5/4 and θ is an acute angle, find the value of 3 sin θ+5 tan θ/6 sin θ+9 tan θ​

Answer 1

Answer:

Given: sec θ=

4

5

secθ=

(4k)

5k

=

4

5

and cosθ=

5

4

Where k is any positive.

By pythagoras theorem:

AC

2

=AB

2

+BC

2

BC

2

=AC

2

−AB

2

=25k

2

+16k

2

BC=3k

Find sinθ,tanθ and cotθ using their definitions:

sinθ=

hypotenuse

perpendicular

=

5

3

tanθ=

base

perpendicular

=

4

3

cotθ=

tanθ

1

=

3

4

Now,

LHS =(

tanθ−cotθ

sinθ−2cosθ

)

=

4

3

−

3

4

5

3

−2×

5

4

LHS=

12

9−16

5

3−8

LHS=

7

12

LHS=RHS