10-350
1f 4tano=3 then Evalvate:-
4 sing-cos&+1.
4 sino +coso-1
Answers
Step-by-step explanation:
We have,
4 than \theta = 34thanθ=3
\implies tan \theta = \frac{3}{4}⟹tanθ=
4
3
\implies sin \theta = \frac{3}{\sqrt{ 3^2 + 4^2}}=\frac{3}{\sqrt{9+16}}=\frac{3}{sqrt{25}}=\frac{3}{5}⟹sinθ=
3
2
+4
2
3
=
9+16
3
=
sqrt25
3
=
5
3
Similarly,
cos \theta = \frac{4}{5}cosθ=
5
4
Thus,
\frac{4 sin \theta - cos \theta + 1}{4 sin \theta + cos \theta - 1}
4sinθ+cosθ−1
4sinθ−cosθ+1
=\frac{4\times \frac{3}{5}-\frac{4}{5}+1}{4\times \frac{3}{5}+ \frac{4}{5} - 1}=
4×
5
3
+
5
4
−1
4×
5
3
−
5
4
+1
=\frac{\frac{12}{5}-\frac{4}{5}+1}{\frac{12}{5}+\frac{4}{5}-1}=
5
12
+
5
4
−1
5
12
−
5
4
+1
=\frac{\frac{12-4+5}{5}}{\frac{12+4-5}{5}}=
5
12+4−5
5
12−4+5
=\frac{13}{11}=
11
13
Hence,
\frac{4 sin \theta - cos \theta + 1}{4 sin \theta + cos \theta - 1}=\frac{13}{11}
4sinθ+cosθ−1
4sinθ−cosθ+1
=
11
13
4tant = 3
tant = 3/4
sint = 3/5
cost = 4/5
4sint - cost + 1 = 4*3/5 - 4/5 + 1
= 12/5 - 4/5 + 1
= (12-4+5)/5
= 13/5
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