## AP State Syllabus SSC 10th Class Maths Solutions 11th Lesson Trigonometry Optional Exercise

AP State Board Syllabus AP SSC 10th Class Maths Textbook Solutions Chapter 11 Trigonometry Optional Exercise Textbook Questions and Answers.

### 10th Class Maths 11th Lesson Trigonometry Optional Exercise Textbook Questions and Answers

Question 1.

Prove that

Answer:

Hence Proved.

Question 2.

Prove that \(\frac{\sin \theta-\cos \theta+1}{\sin \theta+\cos \theta-1}\) = \(\frac{1}{\sec \theta-\tan \theta}\) using the identity sec^{2} θ = 1 + tan^{2} θ.

Answer:

From (1) and (2), we get L.H.S. = R.H.S.

Hence Proved.

Question 3.

Prove that (cosec A – sin A) (sec A – cos A) = \(\frac{1}{\tan A+\cot A}\)

Answer:

L.H.S. = (cosec A – sin A) (sec A – cos A)

Now

From (1) and (2), we get

L.H.S. = R.H.S.

∴ (cosec A – sin A) (sec A – cos A) = \(\frac{1}{\tan A+\cot A}\)

Question 4.

Prove that \(\frac{1+\sec A}{\sec A}\) = \(\frac{\sin ^{2} A}{1-\cos A}\)

Answer:

Question 5.

Prove that \(\left(\frac{1+\tan ^{2} A}{1+\cot ^{2} A}\right)\) = \(\left(\frac{1+\tan A}{1+\cot A}\right)^{2}\) = tan^{2} A

Answer:

Question 6.

Prove that \(\left(\frac{\sec A-1}{\sec A+1}\right)\) = \(\left(\frac{1-\cos A}{1+\cos A}\right)\)

Answer:

∴ L.H.S. = R.H.S.