Question

if m=sin theta+cos theta and n=tan theta+cot theta then prove that n(m^2-1)=2

Answer 1

Hey!

m = Sin∅ + Cos∅

n = tan∅ + cot∅

__________

n = tan∅ + cot∅

[ tan∅ = sin∅/cos∅ and
cot∅ = cos∅/sin∅]

n = sin∅/cos∅ + cos∅/sin∅

n = ( sin²∅ + cos²∅ )/sin∅cos∅

[ sin²∅ + cos²∅ = 1 ]

n = 1/sin∅ cos∅

• Taking LHS

n ( m² - 1 )

1/sin∅cos∅ [ ( sin∅ + cos∅ )² - 1 ]

[ Using identity :- ( a + b )² = a² + b² + 2ab ]

= 1/sin∅cos∅ [ sin²∅ + cos²∅ + 2sin∅cos∅ - 1 ]

= 1/sin∅cos∅ [ 1 + 2sin∅cos∅ - 1 ]

= 1/sin∅cos∅ [ 2sin∅cos∅ ]

= 2

LHS = RHS !!

Hence , proved !!

Answer 2

hey there

here's ur answer.