trigonometry ka question hai please solve

Asked by jaiswalpiyush040 | 20th Jul, 2020, 08:22: AM

Expert Answer:

Given: sin alpha sin beta - cos alpha cos beta + 1 = 0
TO prove: 1 + cot alpha tan beta = 0

sinα space sinβ space minus space cosα space cosβ space plus thin space 1 space equals space 0
minus open parentheses cosα space cosβ space minus space sinα space sinβ close parentheses space plus space 1 space equals space 0
minus cos open parentheses straight alpha plus straight beta close parentheses plus 1 equals 0
rightwards double arrow cos open parentheses straight alpha plus straight beta close parentheses equals 1
Consider comma
1 space plus space cotα space tanβ space equals space 1 plus cosα over sinα cross times sinβ over cosβ
equals fraction numerator sinαcosβ plus cosαsinβ over denominator sinαcosβ end fraction
equals fraction numerator sin open parentheses straight alpha plus straight beta close parentheses over denominator sinαcosβ end fraction
equals fraction numerator square root of 1 minus cos squared open parentheses straight alpha plus straight beta close parentheses end root over denominator sinαcosβ end fraction
equals fraction numerator square root of 1 minus 1 end root over denominator sinαcosβ end fraction space space space space space space space space space space space space space space space space space open square brackets Since comma space cos open parentheses straight alpha plus straight beta close parentheses equals 1 close square brackets
equals 0
Hence comma space 1 plus cotα space tanβ space equals space 0

Answered by Renu Varma | 23rd Jul, 2020, 01:23: PM