cos a – sin a +1 / cos a +.sin a -1 =cosec a +cot a. prove it​

Question

cos a – sin a +1 / cos a +.sin a -1 =cosec a +cot a. prove it​

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Jade 1 month 2021-08-14T20:03:47+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-14T20:05:07+00:00

    Answer:

    cosA-sinA+1/cosA+sinA-1

    =(cosA-sinA+1)(cosA+sinA+1)/(cosA+sinA-1)(cosA+sinA+1)

    =(cos²A-cosAsinA+cosA+cosAsinA-sin²A+sinA+cosA-sinA+1)/{(cosA+sinA)²-(1)²}

    =(cos²A-sin²A+2cosA+1)/(cos²A+2cosAsinA+sin²A-1)

    ={cos²A+2cosA+(1-sin²A)}/(1+2cosAsinA-1) [∵, sin²A+cos²A=1]

    =(cos²A+2cosA+cos²A)/2cosAsinA

    =(2cos²A+2cosA)/2cosAsinA

    =2cosA(cosA+1)/2cosAsinA

    =(cosA+1)/sinA

    =cosA/sinA+1/sinA

    =cotA+cosecA

    =cosecA+cotA (Proved)

    0
    2021-08-14T20:05:46+00:00

    Answer:

    hope this will help you…please mark me as brainliest

    Step-by-step explanation:

    cosA−sinA+1cosA+sinA−1cos⁡A−sin⁡A+1cos⁡A+sin⁡A−1

    =(cosA−sinA+1)(cosA+sinA+1)(cosA+sinA−1)(cosA+sinA+1)=(cos⁡A−sin⁡A+1)(cos⁡A+sin⁡A+1)(cos⁡A+sin⁡A−1)(cos⁡A+sin⁡A+1)

    =(cosA+1¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯−sinA)(cosA+1¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯+sinA)(cosA+sinA¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯−1)(cosA+sinA¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

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