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Q.

If sec4⁡θ+sec2⁡θ=10+tan4⁡θ+tan2⁡θ then sin2⁡θ=

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a

23

b

34

c

45

d

56

answer is C.

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Detailed Solution

sec4⁡θ+sec2⁡θ=10+tan4⁡θ+tan2⁡θ⇒ sec4⁡θ−tan4⁡θ+sec2⁡θ−tan2⁡θ=10⇒ sec2⁡θ+tan2⁡θ+1=10⇒ 2sec2⁡θ=10⇒ cos2⁡θ=15⇒ sin2⁡θ=45
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