Buktikan bahwa cos theta/ (1 + sin theta) + (1 + sin theta)/cos theta = 2 detik theta?

Buktikan bahwa cos theta/ (1 + sin theta) + (1 + sin theta)/cos theta = 2 detik theta?

Kita harus membuktikan cos theta / 1-sin theta + 1-sin theta / cos theta =2 sec theta

Larutan

Mari kita mulai dengan LHS

cos theta / 1-sin theta + 1-sin theta / cos theta

= cos theta * cos theta + 1-sin theta * 1-sin theta / cos theta * 1-sin theta

= cos sq theta + 1+ sin sq theta -2sin theta / cos theta * 1-sin theta

= 2 -2sin theta / cos theta * 1-sin theta

=2(1-sin theta )/ cos theta * 1-sin theta

=2/cos theta

= 2 * 1/cos theta

= 2 detik theta

= RHS

Maka Terbukti

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