Question

If cosec theta + cot theta = p prove that cos theta = p2-1 / p2 + 1

Answer 1

Cosec¢+cot¢=p

=1/sin¢+cos¢/cos¢=p

=1+cos¢/sin¢=p

From Rhs
P^2-1/p^2+1

=(1+cos¢/sin¢) ^2-1/(1+sin¢/cos¢) ^2+1

=1+co¢^2¢+2cos¢-1/cos¢(1+cos^2¢+2cos¢+1/cos¢
=cos¢

Answer 2

Answer:

Step-by-step explanation:

Cosec A + Cot A = P

= 1/Sin A + Cos A / Sin A = P

= 1+Cos A/Sin A = p

=> SQUARING ON BOTH SIDES

= (1+COS A)²/(SINA)²= P²

= (1+ Cos A)² / (Sin A)² = P²

= (1+cos A)² = (p²)[(Sin A)²]

= (1+ cos A) ² = (p²) [(1-cos²A)]

= (1+ cos A) ² = (p²) [ (1+cosA)(1-cos A) ]

= (1+cos A)² ÷ (1+ cos A) = (p²)[(1-cos A)]

= 1+cos A = (p²)[1-cos A]

= 1+cos A ÷ 1-cos A = p²

= Here, Using (a+b/a-b=c+d/c-d). This is known as Componendo and dividendo

According to the Question statement!

1+cos A ÷ 1-cos A = p²

Then,

(1+cos A) + (1 - cos A ) ÷ (1+ Sin A - (1-sin A) = p²+1 / p²-1

= 2/2cos = p²+1/p²-1

= 1/cos = p²+1/p²-1

= Sec = p²+1 /p²-1

We know that Cos A = 1/sec A

Then,

Cos A = p²-1 /p²+1