![{\displaystyle \mathrm {\operatorname {Sin} .^{2}AS=1-\operatorname {Cos} .^{2}AS=1-\operatorname {Cos} .^{2}SH\operatorname {Cos} .^{2}AH} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/ea4fb2ed9b0112ed30b2b6e6113cc3ce2e3ed486)
![{\displaystyle =1-\operatorname {Cos} .^{2}\mathrm {SH{\frac {\operatorname {Cos} .^{2}AC}{\operatorname {Cos} .^{2}CH}}} =\mathrm {\frac {\operatorname {Cos} .^{2}CH-\operatorname {Cos} .^{2}SH\operatorname {Cos} .^{2}AC}{\operatorname {Cos} .^{2}CH}} ,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/602fb1521be11f5c29dce329a5f62f13fffaf388)
![{\displaystyle \mathrm {\operatorname {Sin} .^{2}AH=1-\operatorname {Cos} .^{2}AH=1-{\frac {\operatorname {Cos} .^{2}AC}{\operatorname {Cos} .^{2}CH}}={\frac {\operatorname {Cos} .^{2}CH-\operatorname {Cos} .^{2}AC}{\operatorname {Cos} .^{2}CH}}} .}](https://wikimedia.org/api/rest_v1/media/math/render/svg/82be57932a3f23d8eadff3ff5c071ba6bbb3cd2e)
substituant ces valeurs, en supprimant le dénominateur
alors commun aux deux termes du premier rapport, il viendra
![{\displaystyle \mathrm {\operatorname {Cos} .^{2}CH-\operatorname {Cos} .^{2}SH\operatorname {Cos} .^{2}AC:\operatorname {Cos} .^{2}CH-\operatorname {Cos} .^{2}AC::\operatorname {Sin} .^{2}OS:\operatorname {Sin} .^{2}OH} ,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/014b5ec9fc16adf55ebb3adc755bb481aef9a459)
ou, en comparant la différence des deux premiers termes et la différence des deux derniers au second et au quatrième,
![{\displaystyle \mathrm {\operatorname {Cos} .^{2}AC-\operatorname {Cos} .^{2}SH\operatorname {Cos} .^{2}AC:\operatorname {Cos} .^{2}CH-\operatorname {Cos} .^{2}AC} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/0d9d12f46ccadb85dff75bb582b1f3cd22c65b45)
![{\displaystyle ::\mathrm {\operatorname {Sin} .^{2}OS-\operatorname {Sin} .^{2}OH:\operatorname {Sin} .^{2}OH} \,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/13bc191a5e75d168fde1872332eb07caaeee9d38)
ou bien
![{\displaystyle \mathrm {\operatorname {Cos} .^{2}AC\operatorname {Sin} .^{2}SH:\operatorname {Cos} .^{2}CH-\operatorname {Cos} .^{2}AC::\operatorname {Sin} .^{2}OS-\operatorname {Sin} .^{2}OH:\operatorname {Sin} .^{2}OH} \,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c23db0f1c2619d154b0ebc9fc4127aec5774066c)
ou encore
![{\displaystyle \operatorname {Cos} .^{2}\mathrm {R} \operatorname {Sin} .^{2}(\mathrm {R} +r+\mathrm {D} ):\operatorname {Cos} .^{2}(r+\mathrm {D} )-\operatorname {Cos} .^{2}\mathrm {R} ::}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f771f5be420a5652a79df0e8e7c5a6a73d8fc433)
![{\displaystyle \operatorname {Sin} .^{2}(\mathrm {R+D} )-\operatorname {Sin} .^{2}r:\operatorname {Sin} .^{2}r}](https://wikimedia.org/api/rest_v1/media/math/render/svg/56c6a6c0a91bbfa9140605d38e59fb4d1dff4299)
or,