Question

Tan theta + sec theta minus 1 upon 10 theta minus sec theta minus 1 equal to cos theta whole upon minus 1 sin theta prove

Answer 1

Step-by-step explanation:

Given Tan theta + sec theta minus 1 upon 10 theta minus sec theta minus 1 equal to cos theta whole upon minus 1 sin theta prove

Prove that

sec theta + tan theta – 1 / tan theta – sec theta + 1 = cos theta / 1 – sin theta

• L. h.S :   1/cos theta + sin theta / cos theta – 1 / sin theta / cos theta – 1/cos theta + 1
•                1 + sin theta – cos theta / cos theta / sin theta – 1 + cos theta / cos theta
•                 1 + sin theta – cos theta / sin theta – 1 + cos theta
•                Multiply both numerator and denominator by 1 – sin theta
• 1 – sin theta + sin theta – sin^2 theta – cos theta + sin theta cos theta / (sin theta – 1 + cos theta) (1 – sin theta)
•         Cos^2 theta – cos theta + sin theta cos theta / (sin theta – 1 + cos theta)(1 – sin theta)
•          Cos theta (cos theta – 1 + sin theta) / (sin theta – 1 + cos theta ) (1 – sin theta)
•                    Cos theta / 1 – sin theta = R. h.S (proved)

Reference link will be

https://brainly.in/question/6523952