√sec²thita+cosec²thita=tan thita +cot thita
Answers
Answered by
0
Answer:
We use the following trigonometric identities:
sec
2
θ=tan
2
θ+1 and
cosec
2
θ=cot
2
θ+1
On adding these, we get:
sec
2
θ+cosec
2
θ=tan
2
θ+cot
2
θ+2
⇒sec
2
θ+cosec
2
θ=tan
2
θ+cot
2
θ+2tanθcotθ=(tanθ+cotθ)
2
⇒
sec
2
θ+cosec
2
θ
=tanθ+cotθ
Hence Proved.
Answered by
0
Step-by-step explanation:
= √sec^2thita + cosec^2thita =
tan thita + cot thita
Squaring both LHS and RHS
= sec^2thita + cosec^2thita =
(tan thita + cot thita)^2
= sec^2thita + cosec^2thita =
tan^2thita + cot^2thita + 2(tan thita)(cotthita)
= sec^2thita + cot^2thita - tan^2thita - cot^2thita = 2(tan thita)(cot thita)
= (sec^2thita - tan^2thita) +
(cosec^2thita - cot^2thita) = 2(1)
= (1) + (1) = 2(1)
Hence proved
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