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Evaluate :
(i)
(ii)
(iii)
(iv)
(i)
(ii)
(iii)
= sin 42° − sin 42°
= 0
(iv) cosec 31° − sec 59° = cosec (90° − 59°) − sec 59°
= sec 59° − sec 59°
= 0
Show that:
(i)
(ii)
(I) tan 48° tan 23° tan 42° tan 67°
= tan (90° − 42°) tan (90° − 67°) tan 42° tan 67°
= cot 42° cot 67° tan 42° tan 67°
= (cot 42° tan 42°) (cot 67° tan 67°)
= (1) (1)
= 1
(II) cos 38° cos 52° − sin 38° sin 52°
= cos (90° − 52°) cos (90°−38°) − sin 38° sin 52°
= sin 52° sin 38° − sin 38° sin 52°
= 0
If , where 2A is an acute angle, find the value of A.
Given that,
tan 2A = cot (A− 18°)
cot (90° − 2A) = cot (A −18°)
90° − 2A = A− 18°
108° = 3A
A = 36°
If tan A = cot B, prove that A + B = .
Given that,
tan A = cot B
tan A = tan (90° − B)
A = 90° − B
A + B = 90°
If , where 4A is an acute angle, find the value of A.
Given that,
sec 4A = cosec (A − 20°)
cosec (90° − 4A) = cosec (A − 20°)
90° − 4A= A− 20°
110° = 5A
A = 22°
If A, B and C are interior angles of a triangle ABC, then show that:
We know that for a triangle ABC,
∠ A + ∠B + ∠C = 180°
∠B + ∠C= 180° − ∠A
Express in terms of trigonometric ratios of angles between
and
.
sin 67° + cos 75°
= sin (90° − 23°) + cos (90° − 15°)
= cos 23° + sin 15°
Hence the angles are between 0 and 45.
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