Chapter 7: Q.30 (page 473)

Establish the identity: $(c s c (θ) - c o t (θ)) (c s c (θ) + c o t (θ)) = 1$

Short Answer

Expert verified

We establish the identity $(c s c (θ) - c o t (θ)) (c s c (θ) + c o t (θ)) = 1$

Step by step solution

Given information

We are given an expression $(c s c (θ) - c o t (θ)) (c s c (θ) + c o t (θ))$

Use algebraic formula (a-b)(a+b)=a2-b2

We get,

$(c s c (θ) - c o t (θ)) (c s c (θ) + c o t (θ)) = c s c^{2} (θ) - c o t^{2} (θ) W e k n o w t h a t 1 + c o t^{2} (θ) = c s c^{2} (θ) ∴ c s c^{2} (θ) - c o t^{2} (θ) = 1$

Conclusion

We establish the identity $(c s c (θ) - c o t (θ)) (c s c (θ) + c o t (θ)) = 1$

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Establish the identity: $(c s c (θ) - c o t (θ)) (c s c (θ) + c o t (θ)) = 1$

Short Answer

Step by step solution

Given information

Use algebraic formula (a-b)(a+b)=a2-b2

Conclusion

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Establish the identity:(csc(θ)-cot(θ))(csc(θ)+cot(θ))=1

Short Answer

Step by step solution

Given information

Use algebraic formula (a-b)(a+b)=a2-b2

Conclusion

One App. One Place for Learning.

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Establish the identity: $(c s c (θ) - c o t (θ)) (c s c (θ) + c o t (θ)) = 1$