Question

CosA (1-CosA + Cos²A) - Cos²A(CosA-1)​

Answer 1

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cosA(1+sinA)+cosA(1-sinA)/(1-sinA)(1+sinA)=4

cosA(1+sinA+1-sinA)/1-sin²A=4

cosA(2)/cos²A=4  [as sin²A+cos²A=1]

2/cosA=4

1/cosA=2

cosA=1/2

cosA=cos60°

∴A=60°

Answer 2

Answer:

$\mathrm{\cos \left(a\right)\left(1-\cos \left(a\right)+\cos ^2\left(a\right)\right)-\cos ^2\left(a\right)\left(\cos \left(a\right)-1\right)=\cos \left(a\right)}$

Step-by-step explanation:

$\mathrm{\cos \left(a\right)\left(1-\cos \left(a\right)+\cos ^2\left(a\right)\right)-\cos ^2\left(a\right)\left(\cos \left(a\right)-1\right)}$

$\mathrm{=\cos \left(a\right)-\cos ^2\left(a\right)+\cos ^3\left(a\right)-\cos ^2\left(a\right)\left(\cos \left(a\right)-1\right)}$

$\mathrm{=\cos \left(a\right)-\cos ^2\left(a\right)+\cos ^3\left(a\right)-\cos ^3\left(a\right)+\cos ^2\left(a\right)}$

$\mathrm{=\cos \left(a\right)}$