Question

if 4 tan theta =3 , compute 4 sin theta - cos theta +1/ 4 sin theta + cos theta + 1​

Answer 1

Step-by-step explanation:

Let ∠A be '∅' (see figure.)

4tan∅ = 34tan∅=3

tan∅ = \frac{3}{4}tan∅=

4

3

\frac{Opposite}{Adjacent} = \frac{3}{4}

Adjacent

Opposite

=

4

3

So, hypothenuse will be 5 by Pythagoras theorem.

Now,

\frac{4sin∅ - cos∅ + 1}{4sin∅ + cos∅ - 1}

4sin∅+cos∅−1

4sin∅−cos∅+1

\frac{ 4 * \frac{3}{5} - \frac{4}{5} + 1 }{ 4 * \frac{3}{5} + \frac{4}{5} - 1 }

4∗

5

3

+

5

4

−1

4∗

5

3

−

5

4

+1

\frac{ \frac{12- 4 + 5}{5} }{ \frac{12 +4 - 5}{5}}

5

12+4−5

5

12−4+5

5 will cancel out,

= \frac{13}{11}=

11

13

= 1.18=1.18

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