Establish the identity. 1-sin theta/1+ sin theta = (tan theta - sec theta)^2 Sta

Question

Establish the identity. 1-sin theta/1+ sin theta = (tan theta - sec theta)^2 Starting with the right side, which shows the key steps in establishing the identity? (tan theta - sec theta)^2 = tan^2 - sec^2 theta = (sin theta - 1)^2/1-sin^2 theta = 1-sin theta/1+sin theta (tan theta - sec theta)^2 = tan^2 - sec^2 theta = (sin theta - 1)^2/1-cos^2 theta = 1-sin theta/1+sin theta (tan theta - sec theta)^2 - sin^2 theta/coss^2 theta - 2 sin theta/cos^2 theta + 1/cos^2 theta = (sin theta-1)^2/1- cos^2 theta = 1 - sin theta/1 + sin theta (tan theta - sec theta)^2 - sin^2 theta/coss^2 theta - 2 sin theta/cos^2 theta + 1/cos^2 theta = (sin theta-1)^2/1- sin^2 theta = 1 - sin theta/1 + sin theta

Explanation / Answer

(1-sin theta)/(1+sin theta)= (sec theta - tan theta)2

Starting with the right side

(tan theta - sec theta)2

sec theta=1/cos theta   and    tan theta= sin theta/cos theta

(sin theta/cos theta - 1/cos theta)2 = (sin theta-1)2/cos2theta

                                                              = (sin theta -1)2/(1-sin2theta)= (1-sin theta)2/(1-sin theta)(1+sin theta)

                                                                                                                 =(1-sin theta)/(1+sin theta)

The correct option is D

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.