Question

If tan A = 1, find the value of 3 sin A-4 cos'A+5
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Answer 1

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

⇒ 5 16

−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 2

Answer:

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