Can someone please explain this trig identity 2pie integrate pie .pdf

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Can someone please explain this trig identity? 2/pie integrate pie _0 cosx sinx dx 1/pie integrate pie_0 2sinx cosx dx 1/pie integrate pie _0[sin(n+1)x+sin(n-1)x]dx 1/pie[-cos(n+1)x/n+1-cos(n- 1)x/n-1]^pie_0 Solution at the second step of the integration, we have taken 2 inside the integration with the sin(nx) because, we wanted to make it an identity. So, coming to the third step now, you must be wondering that how did we get sin(n+1)x and sin(n-1)x suddenly ! right ? So, here it goes : there is one identity: 2sin(a)cos(b) = sin(a+b) + sin(a-b) So, now things become easier, right? so, now we can easily write the conversion from second step to the third step: so, 2sin(nx).cos(x) becomes sin(nx+x)+sin(nx-x) = sin((n+1)x)+sin((n-1)x) Hope i made the things clear. Thanks! Have a good day ! :D and happy problem solving !.

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What’s Love Got To Do With It? The Evolution of Human Mating By Meredith F. Small Reviewed By Michael S. Kimmel When Tina Turner first bitterly asked “What’s love got to do with it?” her voice was so drenched with pain and regret, the listener knew better than to believe her. Not so Meredith Small. A physical anthropologist whose main research has been on primate mating behavior, Small joins a coterie of such writers as Robert Ardrey, Desmond Morris and Lionel Tiger, who have sought to make evolutionary biology the foundation of studies of sexual behavior. In “What’s Love Got To Do With It,” Small argues that we’re genetically programmed to experience sexual pleasure; hard-wired to search for young, attractive mates; driven to copulate “Way down deep, underneath all the love and lust, underlying the attachment and intimacy, is DNA pushing us along” Like those male writers, she claims that our genetic predisposition toward reproductive success is the driving force of our sex-seeking behavior. And like them, she assumes that sex is a constant, universal and relatively unchanging experience. But unlike them, Small places no value on judgments on the strategies that individuals may adopt to achieve that reproductive success. Women, she argues, are as sexual as men; homosexuality is as “normal” as heterosexuality. Small exposes many of her colleagues’ conclusions as based more on myth than on evolution. Take, for example, the familiar canard that men are “naturally” predisposed toward promiscuity, while women are “naturally” monogamous. Males’ prodigious sperm production, the argument goes, means that it is in men’s interest to fertilize as many women as possible. But women produce only one egg at a time, and gestation and child care take an extraordinarily long time, which means that it is in their interest to mate with only one man for life. Not only do such arguments assume what they are trying to explain, but their assumptions are wrong to begin with. Sperm and eggs do not have little personalities, complete with ambitions and motivations. What’s more, the evidence actually tilts the other way. Female humans are among the only mammals who conceal estrus; that is, they do not go into “heat” when they are sexually receptive. They are potentially sexually receptive all through their cycle. What’s more, a woman has a clitoris, which “exists only to receive and give off sexual pleasure.” What could be the evolutionary function of that? Small argues that it is just as likely that women may be designed to maximize their reproductive chances by promiscuity. If they have sex with a large number of male partners, they can ensure that their offspring will have a significant number of men who believe that they are the father, and who will, therefore, protect the baby and provide it with food. “The ability to move from male to male certainly improves a female’s chance of finding the best genes for her future offspring,” Small writes. Males, by contrast, wo.

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