Question

Write the expression in rectangular form, X+yi, and in exponential form. re
(-1 + 2)​

Answer 1

Answer:

$EXPLANATION.</p><p>[tex]\sf \implies \dfrac{cos(A)}{1 - tan(A)} \ + \ \dfrac{sin(A)}{1 - cot(A)} = sin(A) + cos(A).$

As we know that,

Formula of :

⇒ tanθ = sinθ/cosθ.

⇒ cotθ = cosθ/sinθ.

Using this formula in equation, we get.

$\sf \implies \dfrac{cos(A)}{1 - \dfrac{sin(A)}{cos(A)} } \ + \ \dfrac{sin(A)}{1 - \dfrac{cos(A)}{sin(A)} }$

$\sf \implies \dfrac{cos(A)}{\dfrac{cos(A) - sin(A)}{cos(A)} } \ + \ \dfrac{sin(A)}{\dfrac{sin(A) - cos(A)}{sin(A)} }$

$\sf \implies \dfrac{cos^{2} (A)}{cos(A) - sin(A)} \ + \ \dfrac{sin^{2} (A)}{sin(A) - cos(A)}$

$\sf \implies \dfrac{cos^{2} (A)}{cos(A) - sin(A)} \ - \ \dfrac{sin^{2} (A)}{cos(A) - sin(A)}$

$\sf \implies \dfrac{cos^{2}(A) - sin^{2} (A) }{cos(A) - sin(A)}$

$\sf \implies \dfrac{[cos(A) - sin(A)][cos(A) + sin(A)]}{cos(A) - sin(A)}$

$\sf \implies cos(A) + sin(A).$

                                                                                                                       

MORE INFORMATION.

Fundamental trigonometric identities.

(1) = sin²θ + cos²θ = 1.

(2) = 1 + tan²θ = sec²θ.

(3) = 1 + cot²θ = cosec²θ.[/tex]