prove that (secA secB + tanA tanB)2 - (secA tanB +tanA secB)2 = 1 - Maths - Trigonometric Functions

Question

prove that (secA secB + tanA tanB)2 - (secA tanB
+tanA secB)2 = 1

Priyanka Kedia · Accepted Answer

L H S
=secAsecB+tanAtanB2-secAtanB+tanAsecB2            =sec2Asec2B+tan2Atan2B+2secAsecBtanAtanB-sec2Atan2B+tan2Asec2B+2secAsecBtanAtanB            =sec2Asec2B+tan2Atan2B+2secAsecBtanAtanB-sec2Atan2B-tan2Asec2B-2secAsecBtanAtanB            =sec2Asec2B+tan2Atan2B-sec2Atan2B-tan2Asec2B            =sec2Asec2B-sec2Atan2B+tan2Atan2B-tan2Asec2B            =sec2Asec2B-tan2B-tan2Asec2B-tan2B            =sec2B-tan2Bsec2A-tan2A            =1×1            =1            =R
H S Hence Proved