Class 9 SELINA Solutions Maths Chapter 25 - Complementary Angles

Ex. 25

Complementary Angles Exercise Ex. 25

Solution 1(i)

Solution 1(ii)

Solution 1(iii)

Solution 1(iv)

Solution 1(v)

$sin squared space 40 degree minus cos squared space 50 equals sin squared space left parenthesis 90 degree minus 50 degree right parenthesis minus cos squared space 50 degree equals cos squared space 50 degree minus cos squared space 50 degree equals 0$

Solution 1(vi)

Solution 1(vii)

Solution 1(viii)

Solution 2(i)

Solution 2(ii)

Solution 2(iii)

Solution 2(iv)

Solution 2(v)

Solution 2(vi)

Solution 3(i)

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.

Solution 3(ii)

Solution 4

Solution 5

(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

Solution 6

(i)

$left parenthesis ii right parenthesis space space 3 cos space 80 degree space cosec space 10 degree plus 2 sin space 59 degree space sec space 31 degree equals 3 cos space left parenthesis 90 degree minus 10 degree right parenthesis space cosec space 10 degree plus 2 sin space left parenthesis 90 degree minus 31 right parenthesis space sec space 31 degree equals 3 sin space 10 degree cosec space 10 degree plus 2 cos space 31 degree space sec space 31 degree equals 3 cross times 1 plus 2 cross times 1 equals 3 plus 2 equals 5$