Class 9 SELINA Solutions Maths Chapter 23 - Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios] Exercise Ex. 23(A)
Solution 1
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Solution 2
(i) 
(ii) 
(iii) 3 sin2 30o + 2 tan2 60o - 5 cos2 45o
Solution 3
(i) LHS=sin 60o cos 30o + cos 60o. sin 30o
=
(ii) LHS=cos 30o. cos 60o - sin 30o. sin 60o
=
=RHS
(iii) LHS= cosec2 45o - cot2 45o
=
=RHS
(iv) LHS= cos2 30o - sin2 30o
=
=RHS
(v) LHS= 
=
=RHS
(vi) LHS= 
=
=RHS
Solution 4
(i)
(ii)
(iii)
Solution 5
Given that AB = BC = x
(i) 
(ii)
(iii)
Solution 6
Solution 7
(i)
The angle, x is acute and hence we have, 0 < x
(ii)
(iii)
(iv)
Solution 8
(i)
if x and y are acute angles,
is false.
(ii)
Sec
. Cot = cosec is true
(iii)
Solution 9
(i)
For acute angles, remember what sine means: opposite over hypotenuse. If we increase the angle, then the opposite side gets larger. That means "opposite/hypotenuse" gets larger or increases.
(ii)
For acute angles, remember what cosine means: base over hypotenuse. If we increase the angle, then the hypotenuse side gets larger. That means "base/hypotenuse" gets smaller or decreases.
(iii)
For acute angles, remember what tangent means: opposite over base. If we decrease the angle, then the opposite side gets smaller. That means "opposite /base" gets decreases.
Solution 10
(i)
(ii) 
Solution 11
(i) Given that A=
(ii)
Given that B=
Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios] Exercise Ex. 23(B)
Solution 1
Given A = 60o and B = 30o
(i)
(ii)
(iii)
(iv)
Solution 2
Given A=
(i)
(ii)
(iii)
(iv)
Solution 3
Given that A = B = 45o
(i)
(ii)
Solution 4
Given that A = 30o
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios] Exercise Ex. 23(C)
Solution 1
(i)
(ii)
(iii)
(iv)
(V)
(vi)
(vii)
(viii)
Solution 2
(i)
(ii)
(iii)
(iv)
(v)
Solution 3
(i)
(ii)
(iii)
Solution 4
(i)
(ii)
(iii)
Solution 5
Solution 6
(i)
(ii)
(iii)
Solution 7
(i)
(ii)
(iii)
Solution 8
(i)
Given that x = 30o
(ii)
Given that B = 90o
Solution 9
(i)
(ii)
(iii)
(iv)
Solution 10
(i)
(ii)
(iii)
(iv)
Solution 11
(i)
(ii)
(iii)
(iv)
Solution 12
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
(ix)
(x)
(xi)
(xii)
Solution 13
(i)
(ii)
(iii)
(iv)
Solution 14
(i)
From
(ii)
(iii)
(iv)
Solution 15
Adding (1) and (2)
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