Chapter 7: Q.17 (page 473)

Factor and simplify: $\frac{3 \sin^{2} (θ) + 4 \sin (θ) + 1}{\sin^{2} (θ) + 2 \sin (θ) + 1}$

Short Answer

Expert verified

The simplified expression can be given as

$\frac{3 \sin (θ) + 1}{\sin (θ) + 1}$

Step by step solution

Given information

We are given am expression $\frac{3 \sin^{2} (θ) + 4 \sin (θ) + 1}{\sin^{2} (θ) + 2 \sin (θ) + 1}$

We factorize and simplify

We get,

$\frac{3 \sin^{2} (θ) + 4 \sin (θ) + 1}{\sin^{2} (θ) + 2 \sin (θ) + 1} = \frac{3 \sin^{2} (θ) + 3 \sin (θ) + \sin (θ) + 1}{(1 + \sin {(θ))}^{2}} = \frac{3 \sin (θ) (\sin (θ) + 1) + (\sin (θ) + 1)}{(1 + \sin {(θ))}^{2}} = \frac{(3 \sin (θ) + 1) (1 + \sin (θ))}{(1 + \sin {(θ))}^{2}} = \frac{3 \sin (θ) + 1}{1 + \sin (θ)}$

Conclusion

The simplified expression can be given as

$\frac{3 \sin (θ) + 1}{\sin (θ) + 1}$ .

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Factor and simplify: $\frac{3 \sin^{2} (θ) + 4 \sin (θ) + 1}{\sin^{2} (θ) + 2 \sin (θ) + 1}$

Short Answer

Step by step solution

Given information

We factorize and simplify

Conclusion

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Factor and simplify:3sin2(θ)+4sin(θ)+1sin2(θ)+2sin(θ)+1

Short Answer

Step by step solution

Given information

We factorize and simplify

Conclusion

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Factor and simplify: $\frac{3 \sin^{2} (θ) + 4 \sin (θ) + 1}{\sin^{2} (θ) + 2 \sin (θ) + 1}$