Direction: Study the following questions carefully and choose the right answer:
1
Find the value of  tan 69° + tan 66° .
1 – tan69° tan66°
» Explain it
B

tan 69° + tan 66°  
1 – tan69° tan66°

= tan(69°+ 66°) = tan135°

= tan(90°+ 45°) = – cot 45° = –1.

Hence, option B is correct.

2
Show that the value of 3 sin 15° – 4 sin3 15° is
» Explain it
C

Using the formula

3 sinΘ – 4 sin3Θ 

=  sin 3 Θ and putting Θ

= 15°

we get: 3 sin 15° – 4 sin3 15°

=  sin(3 × 15°)  = sin 45°  =   1 .
2

Hence, option C is correct.

3
Evaluate: cos2 45° - sin2 15°.
» Explain it
C

We know that

cos2 Θ - sin2 Φ = cos (Θ + Φ). cos(Θ - Φ).

∴     cos2 45° - sin2 15° =

       cos (45° + 15°). cos (45° - 15°)

=   cos 60° . cos 30° =   1  × 
3
 = 
3
.
2 2 4

Hence, option C is correct.

4
What is the value of sin 79° cos 19° – cos 79° sin 19°.
» Explain it
A
sin 79° cos 19° – cos 79° sin 19°

By the formula,

sin(x – y) = sin(x) cos(y) – cos(x) sin(y)

= sin (79° - 19°) = sin 60°.

=  
3
.
2

Hence, option A is correct.

5
What is the value of cos 70° cos 40° + sin 70° sin 40° ?
» Explain it
C
cos 70° cos 40° + sin 70° sin 40° = cos(70° – 40°)

= cos 30° =
3
 
2

[because cos x cos y – sin x sin y = cos (x – y)]

Hence, option C is correct.