if sin Theta=4/5 find the value of 4tan theta-5coa theta sec theta + 4cit theta
Answers
Step-by-step explanation:
Given :-
Sin θ = 4/5
To find :-
Find the value of 4Tan θ-5Cos θ Sec θ+4 Cot θ ?
Solution :-
Given that
Sin θ = 4/5
On squaring both sides then
=> (Sin θ )²= (4/5)²
=> Sin² θ = 16/25
On Subtracting above equation from 1 then
=>1- Sin² θ = 1-(16/25)
=> 1- Sin² θ = (25-16)/25
=> 1- Sin² θ = 9/25
We know that
Sin² A + Cos² A = 1
=> Cos² θ = 9/25
=> Cos θ = √(9/25)
Since θ is acute angle then
=> Cos θ = 3/5
We know that
Tan θ = Sin θ / Cos θ
=> Tan θ = (4/5)/(3/5)
=> Tan θ = (4×5)/(3×5)
=> Tan θ = 4/3
and
1/ Tan θ = 1/(4/3)
=> Cot θ = 3/4
Now,
4Tan θ-5Cos θ Sec θ+4 Cot θ
=> 4Tan θ-5Cos θ (1/Cos θ)+4 Cot θ
=> 4Tan θ-5(Cos θ/Cos θ)+4 Cot θ
=> 4Tan θ-5(1)+4 Cot θ
=> 4Tan θ-5+4 Cot θ
=> 4(4/3) -5 +4(3/4)
=> (16/3)-5+(12/4)
=> (16/3)-5+3
=> (16/3) -2
=> (16-6)/3
=> 10/3
Answer:-
The value of 4Tan θ-5Cos θ Sec θ+4 Cot θ is 10/3
Used formulae:-
→ Sin² A + Cos² A = 1
→ Tan θ = Sin θ / Cos θ
→ Sec θ = 1/ Cos θ
→ Cot θ = 1/ Tan θ
Answer:
Given :-
Sin θ = 4/5
To find :-
Find the value of 4Tan θ-5Cos θ Sec θ+4 Cot θ ?
Solution :-
Given that
Sin θ = 4/5
On squaring both sides then
=> (Sin θ )²= (4/5)²
=> Sin² θ = 16/25
On Subtracting above equation from 1 then
=>1- Sin² θ = 1-(16/25)
=> 1- Sin² θ = (25-16)/25
=> 1- Sin² θ = 9/25
We know that
Sin² A + Cos² A = 1
=> Cos² θ = 9/25
=> Cos θ = √(9/25)
Since θ is acute angle then
=> Cos θ = 3/5
We know that
Tan θ = Sin θ / Cos θ
=> Tan θ = (4/5)/(3/5)
=> Tan θ = (4×5)/(3×5)
=> Tan θ = 4/3
and
1/ Tan θ = 1/(4/3)
=> Cot θ = 3/4
Now,
4Tan θ-5Cos θ Sec θ+4 Cot θ
=> 4Tan θ-5Cos θ (1/Cos θ)+4 Cot θ
=> 4Tan θ-5(Cos θ/Cos θ)+4 Cot θ
=> 4Tan θ-5(1)+4 Cot θ
=> 4Tan θ-5+4 Cot θ
=> 4(4/3) -5 +4(3/4)
=> (16/3)-5+(12/4)
=> (16/3)-5+3
=> (16/3) -2
=> (16-6)/3
=> 10/3
Answer:-
The value of 4Tan θ-5Cos θ Sec θ+4 Cot θ is 10/3
Used formulae:-
→ Sin² A + Cos² A = 1
→ Tan θ = Sin θ / Cos θ
→ Sec θ = 1/ Cos θ
→ Cot θ = 1/ Tan θ