If tan A = 1, find the value of 3 sin A-4 cos'A+5
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Answers
Answer:
ANSWER
We have,
4cosθ+3sinθ=5
Then,
4cosθ+3sinθ=5
4cosθ+3
1−cos
2
θ
=5
3
1−cos
2
θ
=5−4cosθ
Squaring both side and we get,
9(1−cos
2
θ)=(5−4cosθ)
2
⇒9−9cos
2
θ=25+16cos
2
θ−40cosθ
⇒25+16cos
2
θ−40cosθ−9+9cos
2
θ=0
⇒25cos
2
θ−40cosθ+16=0
⇒(5cosθ)
2
−2×5cosθ×4+4
2
=0
⇒(5cosθ−4)
2
=0
⇒5cosθ−4=0
⇒5cosθ=4
⇒cosθ= 54
Put the value of given equation and we get,
4cosθ+3sinθ=5
⇒4× 54
+3sinθ=5
⇒ 516 −5=3sinθ
⇒3sinθ= 5
16−25
⇒sinθ=− 159
⇒sinθ= 5−3
Then,
tanθ= cosθ-sinθ
tanθ= 54− 53
tanθ= 4−3
Hence, this is the answer
Step-by-step explanation:
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Answer:
(5√2 - 1)/√2
Step-by-step explanation:
Given, tan A = 1.
Thus, A = 45°.
So, 3 sinA - 4 cosA + 5
=> 3 sin45° - 4 cos45° + 5
=> 3 (1/√2) - 4 (1/√2) + 5
=> 3/√2 - 4/√2 + 5
=> -1/√2 + 5
=> (-1 + 5√2)/√2
=> (5√2 - 1)/√2