**5**

### Trigonometry

**7**

### Transformation

## Questions

### Prove (1+cosθ+sinθ)/(1-cosθ+sinθ) = cotθ/2

please help me how to solve it. this is fustrating :(

### If sin(A/3) = 1/2(a+1/a), prove that: sinA = -1/2(a^3 + 1/a^3)

please help me w/ this

### If costheta = 3/4, find the value of sin2theta

pls help me

### Find the HCF from a^3 - a^2 + a - 1 and 2a^3 - a^2 + a - 2

Hello my friend! How can i solve this?
1st expression:

= a^{3} - a^{2} + a - 1

= ...?
Pls help. Thank u. Nice day!

### Find HCF from m^3 - 8n^3, 2m^2 - 5mn + 2n^2, and 2m^2 - 8n^2

Hello friend, I’ve done few steps for 1st expression, but I can’t solve any further. Can u pls help?
1st expression:

= m^{3} - 8n^{3}

= m^{3} - (2n)^{3}

= (m - 2n)(m^{2} + 2mn + 4n^{2})

= (m - 2n)... ??

### Find HCF of 8x^3 + 4x^2 + 2x, 16x^4 + 4x^2 + 1 and 8x^3 - 1

I am stuck in first expression. I'm not sure how to solve further. Pls help
1st expression = 8x^{3} + 4x^{2} + 2x

= 2x(4x^{2} + 2x + 1)

### Prove: 2sin^2(45 - A) = 1 - 2sinA

How can I solve this? The 45-A is making me so confused. Plz help

### If sinA = 1/2, find the value of sin3A

Can someone pls help me to solve this? I just know that sin2A = 2sinA.cosA, but it doesn't seem like that formula is helpful in this question. I have no idea about what to do for sin3A.

### Prove cos⁴A + sin⁴A = 1 - 1/2(sin²2A)

Can someone please help me to solve this question?
I can't go beyond this:
= cos⁴A + sin⁴A

= (cos^{2}A)^{2} + (sin^{2}A)^{2}

I can't solve it after this :(