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\( cos^2x+sin^2x=1 \)
\( tan^2x + 1 = sec^2x\)
\(cot^2x+1 = cosec^2x \)
\(tanx = \frac{sinx}{cosx} \)
\(cotx=\frac{cosx}{sinx} \)
\(secx= \frac{1}{cosx} \)
\(cosecx=\frac{1}{sinx} \)
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Osborn's Rule: The hyperbolic identities are directly analogous to the trigonometric identities, with a change of sign when we have a \(sin^2x\) term either explicitly or implicitly (e.g. as with \(tan^2x \) )
\( cosh^2x - sinh^2x =1 \)
\( -tanh^2x + 1 = sech^2x\)
\(-coth^2x+1 = -cosech^2x \)
\(tanhx = \frac{sinhx}{coshx} \)
\(cothx=\frac{coshx}{sinhx} \)
\(sechx= \frac{1}{coshx} \)
\(cosechx=\frac{1}{sinhx} \)
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