Chapter 7: Q.15 (page 473)

Multiply and simplify: $\frac{(\sin (θ) + \cos (θ)) (\sin (θ) + \cos (θ)) - 1}{\sin (θ) \cos (θ)}$

Short Answer

Expert verified

On simplifying we get the answer as $2$

Step by step solution

Given information

We are given an equation $\frac{(\sin (θ) + \cos (θ)) (\sin (θ) + \cos (θ)) - 1}{\sin (θ) \cos (θ)}$

Multiply and simplify

We get,

$\frac{(\sin (θ) + \cos (θ)) (\sin (θ) + \cos (θ)) - 1}{\sin (θ) \cos (θ)} = \frac{\sin^{2} (θ) + \cos^{2} (θ) + 2 \sin (θ) \cos (θ) - 1}{\sin (θ) \cos (θ)} = \frac{1 + 2 \sin (θ) \cos (θ) - 1}{\sin (θ) \cos (θ)} = \frac{2 \sin (θ) \cos (θ)}{\sin (θ) \cos (θ)} = 2$

Conclusion

on simplifying we get 2.

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Multiply and simplify: $\frac{(\sin (θ) + \cos (θ)) (\sin (θ) + \cos (θ)) - 1}{\sin (θ) \cos (θ)}$

Short Answer

Step by step solution

Given information

Multiply and simplify

Conclusion

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Multiply and simplify:(sin(θ)+cos(θ))(sin(θ)+cos(θ))-1sin(θ)cos(θ)

Short Answer

Step by step solution

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Conclusion

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Multiply and simplify: $\frac{(\sin (θ) + \cos (θ)) (\sin (θ) + \cos (θ)) - 1}{\sin (θ) \cos (θ)}$