Question

i have a doubt bin half angle formula....how it was derived...I am queries in this formula base question
​

Answer 1

Answer:

okh let me tell you

Step-by-step explanation:

Half angle formulas can be derived from the double angle formulas, particularly, the cosine of double angle. For easy reference, the cosines of double angle are listed below:

 

cos 2θ = 1 - 2sin2 θ   →   Equation (1)

cos 2θ = 2cos2 θ - 1   →   Equation (2)

 

Note that the equations above are identities, meaning, the equations are true for any value of the variable θ. The key on the derivation is to substitute θ with ½ θ.

 

For Equations (1) and (2), let θ = ½ θ

 

From Equation (1)

cos2(12θ)=1−2sin212θcos⁡2(12θ)=1−2sin2⁡12θ

cosθ=1−2sin212θcos⁡θ=1−2sin2⁡12θ

2sin212θ=1−cosθ2sin2⁡12θ=1−cos⁡θ

sin12θ=1−cosθ2−−−−−−−−√sin⁡12θ=1−cos⁡θ2

 

From Equation (2)

cos2(12θ)=2cos212θ−1cos⁡2(12θ)=2cos2⁡12θ−1

cosθ=2cos212θ−1cos⁡θ=2cos2⁡12θ−1

2cos212θ=1+cosθ2cos2⁡12θ=1+cos⁡θ

cos12θ=1+cosθ2−−−−−−−−√cos⁡12θ=1+cos⁡θ2

 

tan12θ=sin12θ

hope this will help you

❤❤❤

Plz mark me as brainliest