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Answer:
L.H.S. = tan 10˚ tan 15˚ tan 75˚ tan 80˚
= tan 10˚ tan 15˚ tan (90˚ – 15˚) tan(90˚ – 10˚)
= tan 10˚ tan 15˚ cot 15˚ cot 10˚
1/cot10˚ × 1/cot 15˚ × cot 15˚ × cot 10˚
= 1 = R.H.S.
Hence proved.
(ii) L.H.S. = cos 1˚ cos 2˚ cos 3˚ …..cos 180˚
= cos1˚ cos2˚ cos 3˚ …..cos 89˚ cos 90˚ ….cos 180˚
= cos 1˚ cos 2˚ cos 3˚ ….cos 89˚ × 0 × cos 91˚ ….cos 180˚
= 0 = R.H.S.
Step-by-step explanation:
(b)x3-3x2-x+3
=x^2(x+3)+1(x+3)
=(x^2+1)(x+3)
(c)AB is the chord of circle with centre O and radius OA
OM is perpendicular to AB
Therefore, AB=48cm
OA=25cm
OM⊥AB
M is the mid-point of AB
AM = 1/2 AB = 1/2×48=24cm
Now right △OAM,
OA
2
=OM
2
+AM
2
(by Pythagoras Axiom)
(25)
2
=OM
2
+(24)
2
OM
2
=(25)
2
−(24)
2
=625−576
=49=(7)
2
OM=7cm
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