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sec 50° + tan 50° is equal to

1) tan 20° + tan 50°

2) 2 tan 20° + tan 50°

3) tan 20° + 2 tan 50°

4) 2 tan 20° + 2 tan 50°

Answer: (3) tan 20° + 2 tan 50°

Solution:

sec 50° + tan 50°

= (1/cos 50°) + tan 50°

= [cos 20°/(cos 20° cos 50°)] + tan 50°

= [sin 70°/(cos 20° cos 50°)] + tan 50°

= [sin(50° + 20°)/ (cos 20° cos 50°)] + tan 50°

= [(sin 50° cos 20° + cos 50° sin 20°)/ (cos 20° cos 50°)] + tan 50°

= [(sin 50° cos 20°)/(cos 20° cos 50°)] + [(cos 50° sin 20°)/(cos 20° cos 50°)] + tan 50°

= tan 50° + tan 20° + tan 50°

= tan 20° + 2 tan 50°

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