Question

If sin thita=5/13 then find:(a)cos thita (b) tan thita (c)cosec thita (d)tan thita+1/cos thita​

Answer 1

Step-by-step explanation:

Given:-

Sinθ = 5/13

To find:-

Find the following

1)Cos θ

2)Tan θ

3)Cosec θ

4)tan θ + 1/ cos θ

Solution:-

Given that :

Sin θ = 5/13

Sin^2 θ = 25/169

We know that Sin^2θ + Cos^2θ = 1

=>(25/169)+ Cos^2 θ = 1

=>Cos^2 θ = 1-(25/169)

=>Cos^2 θ = (169-25)/169

=>Cos^2 θ = 144/169

=>Cos θ = √(144/169)

=>Cos θ = 12/13

Therefore Cos θ = 12/13

1) Cos θ = 12/13

2) we know that

Tan θ = Sin θ/ Cos θ

=> Tan θ = (5/13)/(12/13)

Tan θ = 5/12

3)We know that

Cosec A = 1/ Sin A

Cosec θ = 1/ Sin θ

=>Cosec θ = 1/(5/13)

Cosec θ =13/5

4)Tan θ + 1/ Cos θ

=>(5/12)+1/(12/13)

=>(5/12)+(13/12)

=>(5+13)/12

=>18/12

=>3/2

Tan θ + 1/ Cos θ = 3/2

Answer:-

1)Cos θ = 12/13

2)Tan θ = 5/12

3)Cosec θ =13/5

4)Tan θ + 1/ Cos θ = 3/2

Used formulae:-

• Sin^2θ + Cos^2θ = 1

• Tan θ = Sin θ/ Cos θ

• Cosec θ = 1/ Sin θ

Answer 2

Answer:

(a) 12/13

(b) 5/12

(c) 13/5

(d) 209/156

Step-by-step explanation :

I attached  a page , hope it helps you :)