Question

cos^2ø by sinø + sinø = cosecø​

Answer 1

Step-by-step explanation:

(sin o + cos o ) ( sec o+ cosec o)

=(sin o+ cos o) (1/ cos o + 1/ sin o)

= (sin o + cos o)(sin o+ cos o/sin o. cos o)

=(sin o+ cos o)^2/ sin o . cos o

=1+2sin o cos o/ sin o.cos o

=1/sin o. cos o+2 sin o cos o/ sin o cos o

=1/sin o . 1/cos o+2

=2+cosec o . sin o

MARK AS BRAINLIEST DEAR FRIEND

Answer 2

☆ Question:

=> To prove

cos^2 θ + sin θ = cosec θ

-----------

sin θ

☆ Solution:

♡ LHS:

cos^2 θ + sin θ

-----------

sin θ

By taking LCM ( Least common multiple)

The LCM = sin θ

= cos^2 θ + sin ^2 θ

-------------------------

sin θ

[ =>we know that sin^2θ * cos ^2 θ = 1 ]

= 1

---------

sin θ

=> cosec θ = RHS

hence proved !!!

______________________________

=> More information:( formulae)

• sin^2θ + cos^2=1
• 1+ tan^2θ = sec^2 θ
• 1 + cot ^2 θ = cosec^2 θ

______________________________

☆ Basic formulae in trigonometry:

1) 1/ sin θ = cosec θ

2) 1/ cos θ = sec θ

3) 1/ tan θ = cot θ

_____________________________