Question

If sin theta =m2-n2÷m2+n2 then mn (sectheta+tantheta)=.....

Answer 1

Answer:

cosФ = 2mn/m²+n²

Step-by-step explanation:

sinФ= m²-n²/m²+n²

as we know sinФ= perpendicular/hypotenuse

sinФ= p/h

⇒m²-n²/m²+n²= p/h

⇒p= m²-n² & h= m²+n²

now as we know that this triangle is always a right angle triangle,

so using Pythagoras theorem,

p²+b²=h²

⇒(m²-n²)²+b²= (m²+n²)²

⇒b²= (m²+n²)² - (m²-n²)²

⇒b²= m∧4 +n∧4 +2m²n² - m∧4 -n∧4 +2m²n²

⇒b²= 4m²n²

⇒b= √4m²n²

⇒b= 2mn

cosФ= b/h

=2mn/m²+n²

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