Check the solution to "Establish identity 9sec2θ−5tan2θ=5+4sec2θ"

ringearV

Answered question

2021-09-09

Establish identity

9 \sec^{2} θ - 5 \tan^{2} θ = 5 + 4 \sec^{2} θ

Alannej

Skilled2021-09-10Added 104 answers

Given identity

9 \sec^{2} θ - 5 \tan^{2} θ = 5 + 4 \sec^{2} θ

First from the left-hand side,

9 \sec^{2} θ - 5 \tan^{2} θ

Here use the Pythagorean trigonometry identity,

\tan^{2} θ + 1 = \sec^{2} θ

9 \sec^{2} θ - 5 \tan^{2} θ = 9 \sec^{2} θ - 5 (\sec^{2} θ - 1)

= 9 \sec^{2} θ - 5 \sec^{2} θ + 5

= 5 + 4 \sec^{2} θ

Therefore it is established that the left-hand side equal to the right-hand side quantity.

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

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