Trig Identities Question! (1 Viewer)

[-billiris]

Using the trig rules, prove:

* (1-sinA)(1+cosecA)=cotACosecA

How do you do this? I keep getting stuck.. should I expand it first would it help?

 

[Drongoski]

Using the trig rules, prove:

* (1-sinA)(1+cosecA)=cotACosA

How do you do this? I keep getting stuck.. should I expand it first would it help?

Should be as corrected, I think.

 

[Crisium]

LHS = (1 - sinA)(1 + cosecA)

= 1 + cosecA - sinA - sinAcosecA

Note that cosecA = 1 / sinA and so sinAcosecA would just be sinA x (1 / sinA) = 1

= 1 + cosecA - sinA - 1

= cosecA - sinA

Make a common denominator

= (1 / sinA) - sinA

= (1 / sinA) - (sin^2(A) / sinA)

= (1 - sin^2(A)) / sinA

Since you know that 1 - sin^2(A) is equal to cos^2(A) by rearranging the identity sin^2(A) + cos^2(A) = 1

= cos^2(A) / sin A

= cosA x (cosA / sinA)

Since cosA / sinA = cotA

= cosA x cotA

= cosAcotA

= RHS

 

[Crisium]

Should be as corrected, I think.

Yeah I got that as well