[1 Mark Question Answer]

Question 11 Mark

Prove that : $\cos ^2 A+\frac{1}{1+\cot ^2 A}=1$.

Answer

$\text { LHS }=\cos ^2 A+\frac{1}{\cos e c^2 A}$
$ =\cos ^2 A +\sin ^2 A $
$= \cos^2 A + \sin^2 A$
$= 1$
$= RHS$
Hence proved.

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Question 21 Mark

Prove the following identity :$\left(1-\sin ^2 \theta\right) \sec ^2 \theta=1$

Answer

$\left(1-\sin ^2 \theta\right) \sec ^2 \theta=1$
Consider L.H.S $=\cos ^2 \theta \sec ^2 \theta$
$=\cos ^2 \theta \times \frac{1}{\cos ^2 \theta}=1$
= R.H.S
Hence proved.

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Question 31 Mark

From the trigonometric table, write the values of tan 45°48'.

Answer

Similarly, tan 45°48' = 1.0283.

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Question 41 Mark

From the trigonometric table, write the values of cos 23°17'.

Answer

From the tables of natural cosines, we have cos 23°12' = 0.9191
Mean difference for 5' = 0.0006 (to be subtracted)
cos 23°17' = 0.9185.

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Question 51 Mark

From trigonometric table, write the values of sin 37°19'.

Answer

From the tables of natural sine, we have
sin 37°18' = 0.606
Mean difference for 1' = 0.0002 (to be added)
So, sin 37°19' = 0.6062.

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Question 61 Mark

Using trigonometric table evaluate the following:
tan 78°55' - tan 55°18'

Answer

tan 78°55' - tan 55°18'
= 5.097 - 1.444
= 3.653.

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Question 71 Mark

Using trigonometric table evaluate the following:
cos 64°42' - sin 42°20'

Answer

cos 64°42' - sin 42°20'
= 0.4274 - 0.6734
= - 0.2460
= - 0.2460.

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Question 81 Mark

Using trigonometric table evaluate the following:
sin 64°42' + cos 42°20'

Answer

sin 64°42' + cos 42°20'
= 0.9041 + 0.7392
= 1.6433.

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Question 91 Mark

Using trigonometric table evaluate the following:
tan 25°45' + cot 45°25'.

Answer

tan 25°45' + cot 45°25'.
= 0.482 + 0.986
= 1.468.

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