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Without using table solve the following; cot 75°Tan 90°Cosec 15°
Cot(-75)=-Cot 75⁰Cot(A+B)=( CotA CotB-1)/(CotA+CotB)- Cot 75⁰= -Cot(45⁰+30⁰)= −[(Cot 45⁰Cot30⁰-1)/(Cot45⁰+Cot30⁰)]= -(√3–1)/(1+√3)= (1-√3)/(1+√3)= (1-√3)(1-√3)/(1+√3)(1-√3)=( 4–2√3)/(-2)= √3–2
Cot(-75)=-Cot 75⁰
Cot(A+B)=( CotA CotB-1)/(CotA+CotB)
- Cot 75⁰= -Cot(45⁰+30⁰)
= −[(Cot 45⁰Cot30⁰-1)/(Cot45⁰+Cot30⁰)]
= -(√3–1)/(1+√3)= (1-√3)/(1+√3)
= (1-√3)(1-√3)/(1+√3)(1-√3)
=( 4–2√3)/(-2)
= √3–2
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