In any triangle ABC, show that from Mathematics Trigonometric F

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 Multiple Choice QuestionsShort Answer Type

171.

Find space space space straight capital delta comma space straight r space and space straight R comma when straight a equals 22 comma space straight b equals 28 comma space straight c equals 36

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172. In any triangle ABC, show that

left parenthesis abc right parenthesis space straight s space equals space straight capital delta squared space cosec straight A over 2 cosec straight B over 2 cosec straight C over 2


In ΔABC comma

space space space sin straight A over 2 space equals space square root of fraction numerator left parenthesis straight s minus straight b right parenthesis space left parenthesis straight s minus straight c right parenthesis over denominator bc end fraction end root comma space space space space space space space space space sin straight B over 2 space equals space square root of fraction numerator left parenthesis straight s minus straight c right parenthesis left parenthesis straight s minus straight a right parenthesis over denominator ca end fraction end root comma space space sin straight C over 2 space equals space square root of fraction numerator left parenthesis straight s minus straight a right parenthesis left parenthesis straight s minus straight b right parenthesis over denominator ab end fraction end root

      straight capital delta space equals space square root of straight s left parenthesis straight s minus straight a right parenthesis space left parenthesis straight s minus straight b right parenthesis space left parenthesis straight s minus straight c right parenthesis end root

R.H.S. = straight capital delta squared cosec straight A over 2 cosec straight B over 2 cosec straight C over 2

          = straight s left parenthesis straight s minus straight a right parenthesis space left parenthesis straight s minus straight b right parenthesis space left parenthesis straight s minus straight c right parenthesis space cross times square root of fraction numerator bc over denominator left parenthesis straight s minus straight b right parenthesis space left parenthesis straight s minus straight c right parenthesis end fraction end root space. space square root of fraction numerator ca over denominator left parenthesis straight s minus straight c right parenthesis space left parenthesis straight s minus straight a right parenthesis space end fraction end root. square root of fraction numerator ab over denominator left parenthesis straight s minus straight a right parenthesis left parenthesis straight s minus straight b right parenthesis end fraction end root

          = abc. s

          = L.H.S.
 
 
        

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173.

In any triangle, show that:  4 Rcos straight A over 2 cos straight B over 2 cos straight C over 2 equals straight s

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174. In any triangle ABC, show that

sin space straight A plus sin space straight B plus sin space straight C space equals space fraction numerator straight capital delta over denominator straight r space straight R end fraction
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175. In any triangle ABC, show that

cosA space plus space cosB space plus space cosC space equals space 1 plus straight r over straight R

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 Multiple Choice QuestionsLong Answer Type

176. In any triangle ABC, show that

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Hence, prove that if sides a,b,c are in A.P., cot straight A over 2 comma space cot straight B over 2 space and space cot straight C over 2 are in A.P.
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 Multiple Choice QuestionsShort Answer Type

177.

In triangle ABC, if b = 15 cm, space space cosB space equals space 4 over 5 comma   find R.

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178.

Convert to radian measure:

40 degree space 20 apostrophe

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179.

Convert to radian measure:

40 degree space 15 apostrophe space 36 apostrophe apostrophe


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180.

Convert to radian measure:

22 degree space 30 apostrophe




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