Answer:
Option B and D are correct
Step-by-step explanation:
Option A is incorrect because the correct identity we have is
[tex]sin^2x+cos^2x=1[/tex]
Hence, Option A is incorrect
Option B is correct because we have an identity
[tex]sin^2x+cos^2x=1[/tex]
[tex]\Rightarrow sin^2x=1-cos^2x[/tex]
Hence, Option B is correct
Option C is incorrect because we have an identity
[tex]tan^2x+1=sec^2x[/tex] not [tex]tan^2x=1+sec^2x[/tex]
Hence, Option C is incorrect
Option D is correct because we have an identity
[tex]1+cot^2x=cosec^2x[/tex] which implies [tex]cot^2x=cosec^2x-1[/tex]
Hence, Option D is correct.
The trigonometry identities are: (b) [tex]\sin^2(x) = 1 -\cos^2(x)[/tex] and (d) [tex]\cot^2(x) = \csc^2(x) -1[/tex]
The basic trigonometry identity is:
[tex]\sin^2(x) +\cos^2(x) = 1[/tex]
The above identity means that, options (a) and (c) are false
Subtract both sides by cos^2(x)
So, we have:
[tex]\sin^2(x) = 1 -\cos^2(x)[/tex]
The above means that, option (b) is true
Divide through by cos^2(x)
[tex]1 = \csc^2(x) -\cot^2(x)[/tex]
Rewrite the equation as:
[tex]\cot^2(x) = \csc^2(x) -1[/tex]
Hence, the identities are: (b) [tex]\sin^2(x) = 1 -\cos^2(x)[/tex] and (d) [tex]\cot^2(x) = \csc^2(x) -1[/tex]
Read more about trigonometry identities at:
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