Prove that by setting these two expressions equal to another, the result is an identity: displaystyle{d}={{cos}^{ -{{1}}}{left( sin{{left({L}{T}_{{1}}

jernplate8

jernplate8

Answered question

2020-11-09

Prove that by setting these two expressions equal to another, the result is an identity:
d=cos1(sin(LT1)sin(LT2)+cos(LT1)cos(LT2)cos(ln1ln2))
d=2sin1(sin2(LT1LT22)+cos(LT1)cos(LT2)sin2(ln1ln22))

Answer & Explanation

curwyrm

curwyrm

Skilled2020-11-10Added 87 answers

Concept used:
cosθ=12sin2(θ2)
cos(AB)=cosBcosA+sinBsinA
Proof:
d=2sin1(sin2(LT1LT22)+cos(LT1)cos(LT2)sin2(ln1ln22))
sind2=(sin2(LT1LT22)+cos(LT1)cos(LT2)sin2(ln1ln22))
As,
cosθ=12sin2(θ2)
So,
(sin(LT1)sin(LT2)+cos(LT1)cos(LT2)cos(ln1ln2))
=12(sin2(LT1LT22)+cos(LT1)cos(LT2)sin2(ln1ln22))2
Therefore,
(sin(LT1)sin(LT2)+cos(LT1)cos(LT2)cos(ln1ln2))
=12(sin2(LT1LT22)+cos(LT1)cos(LT2)

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Linear algebra

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?