TanA=12/5 find sinA+CosA=?
Answers
Answer :
Given :-
Tan A = 12/5
To find :-
Find the value of Sin A + Cos A ?
Solution :-
Given that
Tan A = 12/5 -----(1)
On squaring both sides then
=> Tan² A = (12/5)²
=> Tan² A = 144/25
On adding 1 both sides then
=> 1 + Tan² A = 1+(144/25)
=> 1 + Tan² A = (25+144)/25
=> 1 + Tan² A = 169/25
We know that
Sec² A - Tan² A = 1
=> Sec² A = 1 + Tan² A
=> Sec² A = 169/25
=> Sec A= √(169/25)
=> Sec A = 13/5
=> 1/CosA = 13/5
=> Cos A = 5/13 -------(2)
On squaring both sides then
=> Cos² A = (5/13)²
=> Cos² A = 25/169
On Subtracting this from 1 both sides
=> 1 - Cos² A = 1-(25/169)
=> 1 - Cos² A = (169-25)/169
=> 1 - Cos² A = 144/169
We know that
Sin² A + Cos² A = 1
=> 1 - Cos² A = Sin² A
Now,
=> Sin² A = 144/169
=> Sin A =√(144/169)
=> Sin A = 12/13------(3)
Now, Sin A + Cos A
From (2)&(3)
=> (12/13)+(5/13)
=> (12+5)/13
=> 17/13
Answer:-
The value of Sin A + Cos A = 17/13
Used formulae:
- Sec² A - Tan² A = 1
- Sin² A + Cos² A = 1
- Sec A = 1/Cos A
Step-by-step explanation:
draw a triangle and application of tangent gives cos and sine
by solving we get
cosa=5/13. Sina=12/13. ( 12^2+5^2=169=13^2)
sinA+CosA=12+5/13=17/13