The cross method is a factorisation method used for quadratics.
Since the equation is in standard form `(``a``x^2+``b``x+``c``=0)` we can factorise using the cross method.
`2\text(sec)^2A` `-3\text(sec)A` `+1``=0`
To factorise, we need to find two values on the left side that multiply to `2\text(sec)^2A` and two values on the right side that multiply to `1` and, when cross multiplied with the left side values and added together, gives `-3\text(sec)A`
For the left side, `2\text(sec)A` and `\text(sec)A` fit the condition
`2\text(sec)A xx \text(sec)A`
`=`
`2\text(sec)^2A`
For the right side, `-1` and `-1` fit both conditions
To factorise, we need to find two values on the left side that multiply to `2 \text(sin)^2theta` and two values on the right side that multiply to `3 \text(cos)^2theta` and, when cross multiplied with the left side values and added together, gives `7 \text(sin) theta \text(cos) theta`
For the left side, `2 \text(sin) theta` and `\text(sin) theta` fit the condition
`2 \text(sin) theta xx \text(sin) theta`
`=`
`2 \text(sin)^2theta`
For the right side, `\text(cos) theta` and `3 \text(cos) theta` fit both conditions