UPSEE Solved Model Paper 6

We can solve this problem using the trigonometric function of Sum and Difference Compound Angles:
An algebraic sum of two or more angles is called a compound angle
tan (A - B) = tan A - tan B/1 + tanA tanB
By using this formula we can find the answer.
We have

sin79°−sin11°

sin79°+sin11°

sin79°−sin11°

sin79°+sin11°

=

cos11°−sin11°

cos11°+sin11°

(Since , sin (90 - θ) = cos θ ; sin 79° = sin (90 - 11) = cos 11°)
Divide the numerator and denominator by cos 11°
=

cos11°−sin11° cos11°

cos11°+sin11° cos11°

=

1− sin11° cos11°

1+ sin11° cos11°

=

1−tan11°

1+tan11°

=

tan45°−tan11°

1+tan45°×tan11°

(since, tan 45 = 1)
= tan (45° - 11°)
Since

tanA−tanB

1+tanAtanB

= tan (A - B)
= tan 34°
∴

sin79°−sin11°

sin79°+sin11°

= tan 34°