cos^2ø by sinø + sinø = cosecø
Answers
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
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☆ 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 !!!
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=> More information:( formulae)
- sin^2θ + cos^2=1
- 1+ tan^2θ = sec^2 θ
- 1 + cot ^2 θ = cosec^2 θ
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☆ Basic formulae in trigonometry:
1) 1/ sin θ = cosec θ
2) 1/ cos θ = sec θ
3) 1/ tan θ = cot θ
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