Tan ^3 theta / 1+tan ^2 theta + cot^3 theta /1+cot ^2 theta = sec theta × cosec theta - 2sin theta × cos theta
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Answer:
Step-by-step explanation:
Tan*3/1+tan*2 + cot*3/1+cot*2
Sin*3/cos*3÷1+sin*2+cos² + cos³/sin³÷1+cos²/sin²
Sin³/cos³÷ sin²+cos²/cos² + cos³/sin³ ÷ sin² + cos²
Sin³/cos³ ÷ 1/cos² + cos³/sin³ ÷ 1/sin²
Sin³/cos. + cos³/sin
Sin*4+ cos*4 ÷ sin × cos
(Sin²)² + (cos²)² ÷ sin × cos
(Sin²+ cos²)² - 2 sin²×cos² ÷ sin×cos
1-2sin²×cos²÷ sin×cos
1/sin×cos -2sin²×cos²/sin×cos
Sec×cosec - 2sin×cos
Lhs=Rhs
Hence proved
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