# Chapter 25 : Complementary Angles - Selina Solutions for Class 9 Maths ICSE

Mathematics in ICSE Class 9 is one of the most challenging and trickiest subjects of all. It includes complex topics such as logarithms, expansions, indices and Pythagoras Theorem which are difficult to understand for an average student. TopperLearning provides study materials for ICSE Class 9 Mathematics to make the subject easy and help students to clear all their concepts. Our study materials comprise numerous video lessons, question banks, revision notes and sample papers which help achieve success in the examination.

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## Chapter 25 - Complementary Angles Excercise Ex. 25

Question 1 Solution 1 Question 2 Solution 2 Question 3 Solution 3 Question 4 Solution 4 Question 5 Solution 5 Question 6 Solution 6 Question 7 Solution 7 Question 8 Solution 8 Question 9 Solution 9 Question 10 Solution 10 Question 11 Solution 11 Question 12 Solution 12 Question 13 Solution 13 Question 14 Solution 14 Question 15

Show that:

tan 10° tan 15° tan 75° tan 80° = 1

Solution 15

L.H.S.

= tan 10° tan 15° tan 75° tan 80°

= tan (90° - 80°) tan (90° - 75°) tan 75° tan 80°

= cot 80° cot 75 ° tan 75° tan 80°

= (cot 80° tan 80°)(cot 75° tan 75°)

= (1)(1)

= 1

= R.H.S.

Question 16

Show that:

sin 42° sec 48° + cos 42° cosec 48° = 2

Solution 16 Question 17

Express each of the following in terms of angles between 0°and 45°:

(i) sin 59°+ tan 63°

(ii) cosec 68°+ cot 72°

(iii)cos 74°+ sec 67°

Solution 17 Question 18

For triangle ABC, show that:

(i) (ii) Solution 18

(i) We know that for a triangle ABC A + B + C = 180° (ii) We know that for a triangle ABC A + B + C = 180° B + C = 180° - A Question 19

Evaluate:

(i)  (iii)  (iv) (v) (vi) (vii) (viii) (ix) Solution 19

(i)  (iii)  (iv)  (v)  (vi)  (vii)  (viii)  (ix)  Question 20 Solution 20 Question 21

In each case, given below, find the value of angle A, where 0° A 90°.

sin (90° - 3A).cosec 42° = 1

Solution 21 Question 22

In each case, given below, find the value of angle A, where 0° A 90°.

cos (90° - A).sec 77° = 1

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