Thursday

September 18, 2014

September 18, 2014

Posted by **Dirk** on Tuesday, April 17, 2007 at 10:18pm.

csc^2(A/2)=2secA/secA-1

Right Side=(2/cosA)/(1/cosA - 1)

= (2/cosA)/[(1-cosA)/cosA]

=2/cosA x (cosA)/(1-cosA)

=2/(1-cosA)

now recall cos 2X = cos^2 X - sin^2 X and we could say

cos A = cos^2 A/2 - sin^2 A/2 and of course sin^2 A/2 + cos^2 A/2=1

so the above 2/(1 - cosA)

=2/[sin^2 A/2 + cos^2 A/2 - (cos^2 A/2 - sin^2 A/2)]

= 2/(2sin^2 A/2)

= csc^2 A/2

= Left Side

Ok, so just using a different form of the double/half-angle formula allowed you to get the sin and therein getting csc.

Thanks Reiny! For a detailed how to and detailed steps. I will be using this service in the future. Thanks again.

**Answer this Question**

**Related Questions**

Maths - Hi, can someone give me the answer to this question: secA-tanA=1/4. Find...

further mathematics - Let P=(cosA sinA) (sinA cosA) Q=(cosB sinA) (sinB cosA) ...

maths(trigonometry) - prove that sinA-cosA+1/sinA+cosA-1=1/secA-tanA

Trigonometry - Prove that 1-cosA+cosB-cos(A+B)/1+cosA-cosB-cos(A+B) = tanA/2cotA...

Math - If 1-cosA=5/13, prove that 25sinA(sinA - cosA)

Spanish - Choose the grammatically correct sentence. A. Está cosa es un lápiz ...

trig - I need to count this: a) 1-tg^2a/1+ctg^2a, when sina =2/3 b) 1-tg^2a/1-...

math - Sina+cosa=root over cosA

math - Sina+cosa=root over cosA

trig - Please help me how to do this: 1) 1 + sina*cosa / (cosa + sina)^2 = 2) ...