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Trigonometric Functions

Short Answer Type

171.

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

123 Views

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

111 Views

173.

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

102 Views

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

100 Views

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

109 Views

Long 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.

109 Views

Short Answer Type

177.
In triangle ABC, if b = 15 cm, $space space cosB space equals space 4 over 5 comma$ find R.

b = 15 cm, $space space cos space straight B space equals space 4 over 5$

$rightwards double arrow$ $sinB space equals space square root of 1 minus cos squared straight B end root space equals space square root of 1 minus 16 over 25 end root space equals space 3 over 5$

Now, $straight a over sinA space equals space straight b over sinB space equals space straight c over sinC space equals space 2 straight R$

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