Question

Plz help me plz and correctly!!!! only 3 questions plz!!!​ 100 points

Answer 1

Explanation:

6)b) Sin A - x Cos A = 0

Sin A = x Cos A

`(Sin \ A)/(Cos \ A) = x`

`(1)/(x)=(1)/((Sin \ A )/(Cos \ A))=1*(Cos \ A)/(Sin \ A)=(Cos \ A)/(Sin \ A)`

`RHS = x +(1)/(x)\\\\\\`

`= (Sin \ A)/(Cos \ A)+(Cos \ A)/(Sin \ A)\\\\\\=(Sin \ A*Sin \ A)/(Cos \ A*Sin \ A)+(Cos \ A * Cos \ A)/(Sin \ A* Cos \ A)\\\\\\= (Sin^(2) \ A)/(Cos \ A*Sin \ A)+(Cos^(2) \ A)/(Cos \ A* Sin \ A)\\\\= (Sin^(2) \ A+Cos^(2) \ A)/(Cos \ A*Sin \ A)\\\\=(1)/(Cos \A*Sin \ A)\\\\= (1)/(Cos \ A)*(1)/(Sin \ A)\\\\=Sec \ A * Cosec \ A`

= LHS

7a) 1 - Sin A = 1/2

`1 = (1)/(2)+ Sin \ A\\\\1-(1)/(2)=Sin \ A\\\\(1)/(2)=Sin \ A\\`

⇒ A = 30°

Sec² A = Sec² 30° =
`((2)/(√(3)))^(2)=\frac{2^(2)}{(\sqrt{3)^(2)}}=(4)/(3)`

`tan^(2) \ A = tan^(2) 30 = ((1)/(√(3)))^(2) = (1)/(3)`

LHS = 6 Sec² A + 9 tan² A

`= 6*(4)/(3)+9*(1)/(3)\\\\\\=2*4 + 3*1\\\\\\= 8 + 3\\\\= 11 = RHS`