Question

Prove that(cos theta – sintheta+1)/(costheta + sintheta+1)= cosectheta + cottheta​

Answer 1

Answer :-

solving LHS,

→ (cosA - sinA + 1)/(cos A + sinA - 1)

dividing numerator and denominator by sinA

→ (cosA / sinA - sinA/sinA + 1/sinA) / (cosA / sinA + sinA/sinA - 1/sinA)

→ (cot A + cosec A - 1) / (cot A - cosec A + 1)

putting 1 = cosec²A - cot²A in numerator,

→ {cot A + cosec A - (cosec²A - cot²A)} / (cot A - cosec A + 1)

→ using (a² - b²) = (a + b)(a - b)

→ (cotA + cosecA)(1 - cosecA + cotA) / (cot A - cosec A + 1)

→ cotA + cosecA = RHS (proved)

Learn more :-

It sino + tano = m

tano - sino an

Then express the

values of m²-n² in terms

of M and N

https://brainly.in/question/13926306

tanA/(1-cotA) + cotA/(1-tanA)

https://brainly.in/question/16775946