Solved UPSC CDS/OTA Question
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Q · TrigonometryMedium · 45s
If sin₄ A – cos₄ A = 1, find the value of sin₂ 2A + tan₂ 2(a)
TopicTrigonometry
Question Typemultiple choice
DifficultyMedium
Marking+1 / −0.33
Test Duration30 min
Step-by-Step Solution
The complete worked solution.
Every step explained — no skipped algebra.
sin₄ A – cos₄ A = 1
⇒(sin₂ A – cos₂ A).( sin₂ A + cos₂ A) = 1
⇒sin₂ A – cos₂ A = 1
⇒cos 2A = –1
⇒cos₂ 2A = 1
⇒sin₂ 2A = 1 – cos₂ 2A = 1 – 1 = 0
⇒tan₂ 2A = sin₂ 2A/cos₂ 2A = 0/1 = 0
Hence, sin₂ 2A + tan₂ 2A = 0
Final Answer: Option D