化简：1/(1+sin²α)+1/(1+cos²α)+1/(1+sec²α)+1/(csc²α)如题,我实在化不出来

化简：1/(1+sin²α)+1/(1+cos²α)+1/(1+sec²α)+1/(csc²α)如题,我实在化不出来
化简：1/(1+sin²α)+1/(1+cos²α)+1/(1+sec²α)+1/(csc²α)
如题,我实在化不出来

化简：1/(1+sin²α)+1/(1+cos²α)+1/(1+sec²α)+1/(csc²α)如题,我实在化不出来
原式=
1/(1+sin²a)+1/(1+cos²a)+1/[1+(1/cos²a)]+1/[1+(1/sin²a)]
=[1/(1+sin²a)+1/(1+1/sin²a)]+[1/(1+cos²a)+1/(1+1/cos²a)]
=[1/(1+sin²a)+sin²a/(1+sin²a)]+[1/(1+cos²a)+cos²a/(1+cos²a)]
=1+1
=2