Question

12.
If tan35°+cot37º+tan325º = xtan53º+tan 127° then x=​

Answer 1

Answer:

tan35+tan53+tan325_approx1.322 when tan53+tan127_0 so value of X is 1

Answer 2

⇒ tan 35° + cot 37° + tan 325° = x tan 53° + tan 127°

⇒ tan 35° + cot (90° - 53°) + tan (360° - 35°) = x tan 53° + tan (180° - 53°)

⇒ tan 35° + tan 53° - tan 35° = x tan 53° - tan 53°

⇒ tan 53° + tan 53° = x tan 53°

⇒ 2 tan 53° = x tan 53°

⇒ x = 2

Hence, Value of x is 2.

Formulae Used :-

◉ tan (180° - θ) = - tan θ

◉ cot (90° - θ) = tan θ

◉ tan (360° - θ) = - tan θ

Some Other Formulae :-

◉ sin (90° - θ) = cos θ

◉ sin ( 180° - θ) = cos θ

◉ cos (180° - θ) = - sin θ

◉ 1 + cos θ = 2 cos² θ/2

◉ 1 - cos θ = 2 sin² θ/2

◉ sin (A + B) = sinAcosB + cosAsinB

◉ cos (A + B) = cosAcosB - sinAsinB

◉ sin 2θ = 2 sinθcosθ

◉ cos 2θ = cos² θ - sin² θ

There are many other formulae that you can derive instead of mugging them up.

Like the half angles formulae:

⇒ sin ( Some ) = 2 sin ( Some / 2 ) cos ( Some / 2)

e.g.,

• sin (5θ) = 2 sin (5θ/2) cos (5θ/2)