Question

Cosec (90-theta)+xcos theta cot(90-theta) =sin(90-theta)

Answer 1

Given :- Cosec (90 - θ) + x * cos θ cot(90 - θ) = sin(90 - θ) . find x ?

Solution :-

→ Cosec (90 - θ) + x * cos θ cot(90 - θ) = sin(90 - θ)

we know that, (90 - ) is in first quadrant , where all values are + ve and,

• sin (90° - x) = cos x
• cos (90° - x) = sin x
• tan (90° - x) = cot x
• cot (90° - x) = tan x
• sec (90° - x) = cosec x
• cosec (90° - x) = sec x .

putting these values we get,

→ sec θ + x *cos θ * tan θ = cos θ

Now putting :-

• sec x = (1/cos x)
• tan x = (sin x / cos x)

→ (1/cos θ) + x * cos θ * (sin θ / cos θ) = cos θ

→ x * sin θ = cos θ - (1/cos θ)

→ x * sin θ = (cos² θ - 1) / cos θ

putting (cos² x - 1) = (- sin²x) in RHS numerator, we get,

→ x * sin θ = ( - sin² θ) / cos θ

dividing both sides by sin θ we get,

→ x = ( - sin θ ) / (cos θ )

→ x = ( - tan θ) (Ans.)

Similar Questions :-

prove that cosA-sinA+1/cos A+sinA-1=cosecA+cotA

https://brainly.in/question/15100532

help me with this trig.

https://brainly.in/question/18213053