Question

Find the value of sin65°39' + cos24°57' - tan10°10'.
(Refer the trigonometric table for the values)

• A. 1.6348
• B. 1.6384
• C. 1.8634
• D. 1.8364

Answer 1

The correct option is B 1.6384

We can write,
65°39' = 65°36' + 3'
From the table we have, sin65°36' = 0.9107
Mean difference for, 3′ = 4

sin65°36' = 0.9107
+ 3′ = 4 (Mean difference to be added for sine)
____________________
sin65°39' = 0.9111 ... (i)


We can write,
24°57' = 24°54' + 3'
From the table we have, cos24°54' = 0.9070
Mean difference for, 3′ = 4

cos24°54' = 0.9070
3′ = - 4 (Mean difference to be subtracted for cosine)
____________________
cos24°57' = 0.9066 ... (ii)


We can write,
10°10' = 10°6' + 4'
From the table we have, tan10°6' = 0.1781
Mean difference for, 4′ = 12
tan10°6' = 0.1781
+ 4′ = 12 (Mean difference to be added for tan)
____________________
tan10°10' = 0.1793 ... (iii)

Solving equation (i) + (ii) - (iii), we get
sin65°39' + cos24°57' - tan10°10' = 0.9111 + 0.9066 - 0.1793
= 1.6384